Can't move System from one phone to another using twrp? I have a HTC desire 510 (broken) and a HTC desire 510 (rather unharmed). 

I made a backup of the system on the old one to the new one using twrp 3.1.1 to the external sd card.

If I put the sd card in the new phone, I can't restore the backup to the new phone, as the backup is not shown to select in twrp. On the other hand the backup of the stock sw I did on the new phone is available for restore. What can I do?
Found the solution in the thing called „internet“:

(in the following it is assumed, that all backups are stored to a SD card).

TWRP stores backups with a „serial number“ of the phone. i.e. when looking into a SD card, there is a folder called TWRP/BACKUPS. Inside this there are subfolders named after a unique ID for every phone. E.g. CC48TY402141 or something like this. I think TWRP derives this code from the IMEI and possibly from other information on the hardware of the phone. 
Inside such a subfolder all backups from a certain phone ares stored.

To convince TWRP to restore the backup from my old phone to a new phone I had to do the following:
I made a backup of the stock software of my new phone. TWRP then created a new subfolder with the ID for the new phone in TWRP/BACKUPS, and stored the backup of the stock ROM there. Then I moved the backup out of the subfolder from my old phone into the new subfolder. After restarting TWRP the backup from my old phone was available and could be restored to the new phone without any hassle.