Moving SSD & HDD from one MBP to different MBP

Hello everyone,

I currently have a 13" MacBook Pro Early 2011 2.3 GHz Core i5 (MC700LL/A) with a 240GB SSD as boot drive running the latest version of Mavericks (10.9.5) and have the optical bay drive replaced with a 1TB HDD exclusively for storage (books, music, movies, photo, docs, etc), along with 16GB ram. A few weeks ago, my lady friend spilled her coffee entirely on the keyboard, trackpad, fan, etc. but I was able to manage saving both drives and ram from any liquid damage.

I have since then purchased a used 13" Late 2011 2.8 GHz Core i7 (MD314LL/A) that can accept the 16GB ram I already have, but what concerns me is whether I can simply install my SSD & HDD into it. Will there be any issues since it's a different processor?

Even though I have everything backed up through Time Machine in an external hard drive, I would hate to format the SSD and install from backup. If this is the case, I may opt for a clean install instead. I have also been thinking about partitioning the HDD to install Yosemite again, but that's not my priority right now.

Finals are coming up and I want to get this out of the way! Please help, anyone. And if there answers already out there for my question, please link them for me because I had no luck searching.

Much love,

rowleyd