If two coins have the same address generation system then their private keys are the same.
So if you sent coinX to a coinY address then you should use your coinY private key and import that address to coinX - if you can.
If you don't know the private key for coinY (ABD in your example) then you're out of luck.
If for some reason you have the private key but it is being refused, you will have to write code to convert to the correct version.