hi, I understand that you have a vpn with a cisco ASA already raised you already have the objects and the community.
what you want to do is another vpn with the same ip in another firewall that is not the cisco ASA
1.-You already have the objects with the ip chkp and interoperable. (CISCO)
2.- You already have the community.
3.- You already have the domains.
4.- You already have the rules of the vpn
you do not need to modify anything if use the same ip, but for your test something sounds wrong in the routing part you can not have two firewalls with the same public ip, you would present an ip conflict, and this could make you have asymetric routing etc etc.
if you have another public ip you can create the interoperable object and raise your vpn of tests.