Can I transfer logic board MacBook Pro 13" mid 2010 to mid 2009 model?

The 2010 is *better*, but isn’t much better then the 2009. I would look at how much a complete 2012 (and a genuine charger if you’re buying it on eBay) since the cost of a whole unit vs. logic board swap is nearly the same, and the swap requires other modifications. You usually need to repaste the CPU and blow the dust out, but that's pretty common on these.
The other issue is the SATA controller on the 2010 inherits the lack of SATA III support, limiting your SSD compatibility with many modern drives being Fixed III. The other major downside is Sierra isn't dead, but it's day is coming any day at this point (if it hasn't already happened). A cosmetically meh 2012 is a better deal. I’ve discussed this swap before in this answer: Does logic board A1278 of MBP Unibody 2012 compatible with MBP 2009?. However, these tend to be so well discounted to move them you may still be able to buy it cheap due to the condition.
In some cases, let some issues like the optical drive go - take the discount and buy an external drive.

The short version of what needs to be done is you need to replace or reconfigure the LCD assembly (2011/12 has a different WiFi configuration and the card is no longer is part of the display), speakers (2012 has different placement), and you will need to upgrade the RAM to 1600, minimum - the 1333 RAM will not work. It's optional, but the hard drive cable should be replaced, especially if you install an SSD as they tend to have issues unless you do that swap as well. You may also need a heatsink.