Logicboard compatiblity between 2009/2010 models

Lets start off looking to see if the two systems are within the same series using EveryMac:

• Mid 2009 2.26 GHz Core 2 Duo - MacBookPro5,5
• Mid-2010 2.4 GHz Core 2 Duo - MacBookPro6,2

We can see these two systems are not within the same series so the possibility of swapping parts is reduced. Next lets look at some images to see if the physical layout of the logic board is the same:

• MacBook Pro 13" Unibody Mid 2009 Logic Board Replacement
• MacBook Pro 13" Unibody Mid 2010 Logic Board Replacement

While things look the same the trackpad/keyboard cable I believe is wider on the '10 model. As I don't have these two systems in front of me you'll need to check out the connections to see if they are the same. There maybe other differences that would prevent your alterations. So you do risk damaging things if you force things.

Frankly, since you're putting in a less powerful logic board into the newer system here I think it would just be better looking for the correct logic board within the series and then sell the other system to cover some of the cost.