Replace the logic board with a newer models as my died

Its much more flexible with the laptop ranges, but typically, the iMacs are less forgiving. They tend to change too much when going between years.

For starters, the SSDs are not interchangeable between the Late 2012 and the Late 2013 models, but not all models have it, so it may not be a problem for your current configuration.

But the LCD panels are interchangeable, as are the rear housing units, the fans and a few of the other major components. But the power supply is stated as being different. (Late 2012 on its own, then Late 2013-2015 separate. This doesn't always mean its completely different, it may just be Apple specifying it as being different because of a supply chain difference, but its not worth the risk unless its carefully checked as variations in power can cause component damage)

The heatsink design does change on some ranges, but on these 2 models it looks similar.

In essence, there is no documentation to confirm interchangeability of parts, but some ranges are fully interchangeable. These have many similarities, but essentially, you wont know without comparing the boards side my side, then fitting it to test, being certain that all power function are of the same voltage for full compatibility.

Its a risk, but in some cases is the only option for testing a part. Just take care in checking compatibility beforehand before taking it, as the risk is entirely on the engineer doing the work.

I hope this helps.