Simulating RF Remote Button Press via Relay

[twostar]

If the OP already has the A16 then it's much easier to get an external relay board than replacing the A16 with an A16S.  You can get the relay boards from Aliexpress for a few dollars, just make sure that they're high-triggered not low-triggered since most of them are low-triggered for Arduino use (the linked ones are high-triggered).  So what you're doing is converting the wet-contact output to a dry-contact one.