The motherboard is pretty much never the issue if it has the right slot for the card. Case size and layout and power supply is what you want to worry about, do those match what you need to run the card? a 560 will be a big boost over a R7 240.
Why even get that card? It's 4 years old. Unless you are getting it free or very cheap it's not worth it.
Yea GeForce GTX 560 Ti can do the motherboard. And there are big differences. Radeon R7 240 vs GeForce GTX 560 Ti
It can do more better graphic cards than 560.