Put a preinstalled macOS SSD to another MacBook, will this occur any problem?
No, you should never experience problems with this. There will never be any damage from this kind of transfer or by doing a time machine backup after the transfer.

That said, depending on which apps you use, some apps and app licenses may have been tied to hardware information such as the old computer's serial number. I'd recommend using migration assistant from a time machine backup of the 2012 computer to make sure you don't have a problem with these licenses.