The door entry system you have is very clever, not simple as appears to be.
From what you have described, taking one hand set down and replacing it with a brand new one, and the new one not working as it should, but then changing it back to the old one and the old one works is similar to what I had.
Unlike "older/conventional" door entry systems, new systems are "auto addressable" Everything that is required is wired in parallel, then (in the case of fermax) you press a "hidden button" on the handset, go to the external call buttons, tap in the house/flat door number, count 3, and the handset will have been given an address which is stored in the handset memory, so if you move that handset from say flat 1 to flat 29 when ever flat 1 is called the handset in flat 29 will sound, as that handset is programmed as flat 1.
It is very clever as all devices are given an encrypted address, which means, although every thing is in parallel (It also saves considerably on the wiring.) there can never be any crosstalk between handsets, as each device only responds to its own address.
I suspect that the BPT unit you have uses the same principal, but if it has a hidden button, or if it uses a combination of buttons to put it into learning mode, sorry I do not know
, I can only suggest you call BPT