if you already know that it's an FM2 socket, then getting an FM2 socket motherboard will be what you do.
As for one that will fit properly in the PC case you have, as long as the original motherboard follows the standard ATX layout, then an standard ATX motherboard will work.
Just look up FM2 socket compatible motherboards online.
But just to make sure though, when looking at the back of the PC where the I/O is, are the cutouts carved into the case, or is it a big rectangle that has another piece put into it that can be removed?
Because if it can be removed, then you can get any FM2 socket motherboard and throw it in there with it's own I/O shield.
But if the I/O shield is cut into the case, then you'll need to get a replacement board that is exactly the same.
--UPDATE--
The motherboard that comes in that system is uATX form factor, while a standard size ATX board might fit, I wouldn't take that chance, so you either find a uATX FM2 board, or you get an mATX (microATX) motherboard, again, assuming that you can use a removable I/O shield, otherwise, if the I/O shield is cut into the case itself and not removable, then you'll have no choice but to search on eBay for that exact motherboard.
https://www.ebay.com/sch/i.html?_from=R40&_trksid=m570.l1313&_nkw=MSI+MS-7778+%28Jasmine%29+&_sacat=0