Let me guess, when interesting traffic arrives at the Fortigate it is able to successfully start a new VPN tunnel and start passing traffic. However when interesting traffic arrives at the Check Point, IKE negotiations fail in Phase 2 and the traffic cannot pass. Fortigates are similar to Juniper/Sonicwall in that Phase 2 subnet/Proxy-ID proposals presented to it must match its configuration precisely, unlike Cisco and Check Point who will accept a subset of their subnet/Proxy-ID configuration in a Phase 2 proposal. You must adjust the Check Point configuration to present the exact subnet/Proxy-IDs that the Fortigate wants in Phase 2.
Read scenario 1 of this SK: sk108600: VPN Site-to-Site with 3rd party
And this SK for the proper filename of user*def file to edit: sk98239: Location of 'user.def' files on Security Management Server
You pretty much are stuck going down this road with Fortigate/Juniper/Sonicwall and to some degree Palo Alto interoperable VPNs.
Also as noted earlier make sure the Phase 1 and Phase 2 lifetimes match exactly, as Delete SA processing upon tunnel expiration does not always work correctly in an interoperable scenario and can cause tunnel hangs.
Attend my online "Be your Own TAC: Part Deux" CheckMates event
March 27th with sessions for both the EMEA and Americas time zones