[werk_ag]

I might give it a try. There is always merit in simplicity. So I connect Pin 2 of the TX unit on the RX board (that's the 3rd pin from the 9V socket end of the TX unit?) to Pin 2 of the RX unit on the WD board (that's the one labelled "Dat" - the 2nd one from the top of the board?). See sketch attached/below for my understanding.

https://www.dropbox.com/s/5sz9it9ox8wtmq...s.jpg?dl=0

The connections on your picture are correct.

You say "don't use the GND pin of the TX module" for the common GND. So is the arrangement shown in the sketch in green okay?

Any GND point, except the GND pin of the TX module, will be fine.