Example based on following versions:
Former example(s) based on following versions:

That's easy, no screenshots should be required
Check whether VPN-1 (Pro) is enabled
Older versions of Check Point Firewall-1 require a dedicated license for VPN-1.

Define topology and VPN domain

Define IKE properties
Public Key Signatures:
Linux gateway has to be created as "Interoperable Device"

Define topology and VPN domain

Import external OPSEC CA certificate (only needed for Public Key Signatures)
Import a CA certificate as type OPSEC from external, is needed for validating the certificate of a remote FreeS/WAN gateway
Note: disable all CRL retrieving options for this CA, if not available - otherwise related error messages will prevent the use of this CA.Define IKE properties
Public Key Signatures:
The DN string is not similar to the one which can be native extracted using OpenSSL, it needs to be reversed, which can be done (if no '/' is specified in an entry) by executing:
$ openssl x509 -subject -noout -in mycert.pem | sed 's/subject= \///g' | sed 's/\//,/g' | awk -F, '{ for (i = NF; i > 1; i--) printf $i ","; printf $1 "\n" }'
Switch to traditional mode
And create a new policy afterwards

Gateway-to-gateway rulesets
Network-to-network rulesets
Properties of encryption

That's easy, no screenshots should be required - good luck!
Log viewer should display following, after on Linux FreeS/WAN IPSec was restarted (use "fw log -tfln" to get log output on console):14:30:18 accept >eth0 product VPN-1 & FireWall-1 src 1.2.3.5 s_port IKE dst 1.2.3.4 service IKE proto udp rule 014:30:18 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 peer gateway 1.2.3.5 scheme: IKE IKE: Main Mode completion. CookieI cd4facedc444d81c
CookieR 399e1a8b6543e4c2 methods: 3DES + MD5, Pre shared secrets14:30:18 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0xdb3ca7ba dstkeyid 0xd0932dbe peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode Sent Notification: Responder Lifetime CookieI cd4facedc444d81c CookieR 399e1a8b6543e4c2 msgid 39d92aae14:30:18 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0xdb3ca7ba dstkeyid 0xd0932dbe peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode completion CookieI cd4facedc444d81c CookieR 399e1a8b6543e4c2 msgid 39d92aae methods: ESP: 3DES + MD5 IKE
IDs: subnet: 172.16.1.0 (mask= 255.255.255.0) and subnet: 172.16.2.0 (mask= 255.255.255.0)14:30:18 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0xdb3ca7bb dstkeyid 0xd0932dbf peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode Sent Notification: Responder Lifetime CookieI cd4facedc444d81c CookieR 399e1a8b6543e4c2 msgid 881b521b14:30:18 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0xdb3ca7bb dstkeyid 0xd0932dbf peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode completion CookieI cd4facedc444d81c CookieR 399e1a8b6543e4c2 msgid 881b521b methods: ESP: 3DES + MD5 IKE
IDs: host: 1.2.3.4 and host: 1.2.3.5
16Apr2002 16:43:56 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 peer gateway 1.2.3.5 scheme: IKE IKE: Main Mode completion.
CookieI d06d13f95066ba08 CookieR fce7a3180b16f5bd methods: 3DES + MD5, RSA signatures16Apr2002 16:43:56 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0x6c916c22 dstkeyid 0x2764eed3 peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode Sent Notification: Responder Lifetime CookieI d06d13f95066ba08 CookieR fce7a3180b16f5bd msgid 3fe711b616Apr2002 16:43:56 keyinst >daemon src 1.2.3.5 dst 1.2.3.4 srckeyid 0x6c916c22 dstkeyid 0x2764eed3 peer gateway 1.2.3.5 scheme: IKE
IKE: Quick Mode completion CookieI d06d13f95066ba08 CookieR fce7a3180b16f5bd msgid 3fe711b6 methods: ESP: 3DES + MD5 IKE
IDs: host: 1.2.3.4 and host: 1.2.3.5
Edit /etc/ipsec.conf or store a dedicated configuration file in /etc/ipsec.d/
## Gateway-to-gateway: Check Point <-> FreeS/WAN
conn checkpoint-freeswan
type=tunnel
# Left side is Check Point
left=1.2.3.4
# leftnexthop=
# Right side is FreeS/WAN
right=1.2.3.5
# rightnexthop=
keyexchange=ike
auth=esp
auto=start
authby=secret
# Optional specify encryption/hash methods for phase 1 & 2
#ike=aes256-sha1-modp2048
#esp=aes256-sha1
# Disable Perfect Forward Secrecy, if not working proper
#pfs=no
# Optional enable compression (if working)
#compress=yes
conn net-checkpoint-net-freeswan
type=tunnel
left=1.2.3.4
# leftnexthop=
leftsubnet=172.16.1.0/24
right=1.2.3.5
# rightnexthop=
rightsubnet=172.16.2.0/24
keyexchange=ike
auth=esp
auto=start
authby=secret
# Optional specify encryption/hash methods for phase 1 & 2
#ike=aes256-sha1-modp2048
#esp=aes256-sha1
# Disable Perfect Forward Secrecy, if not working proper
#pfs=no
# Optional enable compression (if working)
#compress=yes
Edit /etc/ipsec.secrets
1.2.3.4 1.2.3.5: "verysecret"
Good luck!# service ipsec restart
Mar 25 15:44:58 linux ipsec__plutorun: Starting Pluto subsystem...
Mar 25 15:44:58 linux Pluto[3160]: Starting Pluto (FreeS/WAN Version 1.96)
Mar 25 15:44:59 linux Pluto[3160]: added connection description "net-checkpoint-net-freeswan"
Mar 25 15:44:59 linux Pluto[3160]: added connection description "checkpoint-freeswan"
Mar 25 15:44:59 linux Pluto[3160]: listening for IKE messages
Mar 25 15:44:59 linux Pluto[3160]: adding interface ipsec0/eth0 1.2.3.5
Mar 25 15:44:59 linux Pluto[3160]: loading secrets from "/etc/ipsec.secrets"
Mar 25 15:44:59 linux Pluto[3160]: "net-checkpoint-net-freeswan" #1: initiating Main Mode
Mar 25 15:44:59 linux Pluto[3160]: "net-checkpoint-net-freeswan" #1: ISAKMP SA established
Mar 25 15:44:59 linux Pluto[3160]: "net-checkpoint-net-freeswan" #2: initiating Quick Mode PSK+ENCRYPT+TUNNEL+DISABLEARRIVALCHECK
Mar 25 15:44:59 linux Pluto[3160]: "net-checkpoint-net-freeswan" #2: ignoring informational payload, type IPSEC_RESPONDER_LIFETIME
Mar 25 15:44:59 linux Pluto[3160]: "net-checkpoint-net-freeswan" #2: sent QI2, IPsec SA established
Mar 25 15:44:59 linux Pluto[3160]: "checkpoint-freeswan" #3: initiating Quick Mode PSK+ENCRYPT+TUNNEL+DISABLEARRIVALCHECK
Mar 25 15:44:59 linux Pluto[3160]: "checkpoint-freeswan" #3: ignoring informational payload, type IPSEC_RESPONDER_LIFETIME
Mar 25 15:44:59 linux Pluto[3160]: "checkpoint-freeswan" #3: sent QI2, IPsec SA established
Edit /etc/ipsec.conf or store a dedicated configuration file in /etc/ipsec.d/
## Gateway-to-gateway: Check Point <-> FreeS/WAN X.509
conn freeswan-checkpoint-x509
type=tunnel
# Left side is Check Point
left=1.2.3.4
leftcert=checkpoint-cert.pem
leftrsasigkey=0x0103......
# leftid= # !do not use for Check Point!
# Right side is FreeS/WAN
right=1.2.3.5
rightid="/C=DE/ST=Bavaria/L=Hohenbrunn/O=AERAsec/OU=Lab/CN=Linux/Email=*******"
# As an alternative, the file itself can be specified
#rightcert=freeswan-cert.pem
rightrsasigkey=%cert
# rightnexthop=
keyexchange=ike
auth=esp
pfs=no
auto=start
authby=rsasig
Note: for full functional network to network encryption all permutations have to be configured as topology, too:conn freeswan-checkpoint-x509-net
type=tunnel
# Left side is Check Point
left=1.2.3.4
leftsubnet=net-behind-Check-Point # Right side is FreeS/WAN right=1.2.3.5
...conn net-freeswan-checkpoint-x509
type=tunnel
# Left side is Check Point
left=1.2.3.4
# Right side is FreeS/WAN
right=1.2.3.5
rightsubnet=net-behind-FreeS/WAN ...conn net-freeswan-checkpoint-x509-net
type=tunnel
# Left side is Check Point
left=1.2.3.4
leftsubnet=net-behind-Check-Point # Right side is FreeS/WAN right=1.2.3.5
rightsubnet=net-behind-FreeS/WAN ...
Edit /etc/ipsec.secrets
# Define RSA key
: RSA /etc/ipsec.d/private/freeswan-key.pem "optional key passphrase here"
Good luck!# service ipsec restart
Apr 16 17:15:47 linux Pluto[4269]: Starting Pluto (FreeS/WAN Version 1.96)
Apr 16 17:15:47 linux Pluto[4269]: including X.509 patch (Version 0.9.9)
Apr 16 17:15:47 linux Pluto[4269]: Changing to directory '/etc/ipsec.d/cacerts'
Apr 16 17:15:47 linux Pluto[4269]: loaded cacert file 'checkpoint-internal-ca.pem' (730 bytes)
Apr 16 17:15:47 linux Pluto[4269]: loaded cacert file 'ca-cert.pem' (1968 bytes)
Apr 16 17:15:47 linux Pluto[4269]: Changing to directory '/etc/ipsec.d/crls'
Apr 16 17:15:47 linux Pluto[4269]: loaded crl file 'checkpoint.crl' (556 bytes)
Apr 16 17:15:47 linux Pluto[4269]: loaded crl file 'ca-crl.pem' (772 bytes)
Apr 16 17:15:47 linux Pluto[4269]: loaded my X.509 cert file '/etc/x509cert.der' (1428 bytes)
Apr 16 17:15:47 linux Pluto[4269]: added connection description "freeswan-checkpoint-x509"
Apr 16 17:15:47 linux Pluto[4269]: listening for IKE messages
Apr 16 17:15:47 linux Pluto[4269]: adding interface ipsec0/eth0 1.2.3.5
Apr 16 17:15:47 linux Pluto[4269]: loading secrets from "/etc/ipsec.secrets"
Apr 16 17:15:47 linux Pluto[4269]: loaded private key file '/etc/ipsec.d/private/freeswan-key.pem' (1803 bytes)
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #1: initiating Main Mode
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #1: Peer ID is ID_IPV4_ADDR: '1.2.3.4'
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #1: CRL signature is invalid
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #1: CRL signature is invalid
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #1: ISAKMP SA established
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #2: initiating Quick Mode RSASIG+ENCRYPT+TUNNEL
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #2: ignoring informational payload, type IPSEC_RESPONDER_LIFETIME
Apr 16 17:15:48 linux Pluto[4269]: "freeswan-checkpoint-x509" #2: sent QI2, IPsec SA established