Try to use “relayhost” directive in main.cf.
If the IP of the mail server configured in MX is 1.2.3.4, then then it should look like this

relayhost = 1.2.3.4

On the mail server you have to allow relay from the source server, this is done through “mynetworks” directive
Just find the configuration directive and add your source IP, so if the source IP is 5.6.7.8, then

mynetworks = 127.0.0.0/8

change to

mynetworks = 127.0.0.0/8 5.6.7.8

There might be more entries on that line already, so just add it at the end of line
Restart postfix on both servers and it should work