Good Question! The 2011 Macbook LCD Panel Will Work In A 2012 , But A 2013 Will Not Work In A 2012. As Well, If You Were To Purchase A Full Assembly With The Aluminum And Bezel, The 2011 And 2013 Are Not Compatible With The 2012 Due To Variations In The Small Parts Within The Assembly.
Depending on which flex is actually torn, either the interconnect or the Touch ID is where your solution will be. If the cable on the LCD Plate is torn, you're ok. (iPhone 6 LCD Shield Plate with Sticker and Home Cable) (Take a look here to see if the cable is along this part) But, if the flex on the Touch ID is torn, you're going to have much more of a headache. The reason being is that the cable that connects the board along the LCD shield can be ripped and replaced with no issues. But, if the Touch ID flex is torn, Touch ID will never properly work again as its individually tied to each phone. That said, you can replace the Touch ID and get the home button functionality back, but the biometric aspect will not fully function again without the original part.
For Me, This Issue Indicated A Problem With The Power/Volume Flex Cable. Nothing Looked Physically Wrong With It, But Upon Replacing It, Everything Booted Up And Resolved Perfectly. Upon Trying Other Solutions To Exit Recovery Mode, I Just Kept Getting A Loop. However, Upon Replacing This Flex Cable, It Works!
I'd Advise Against The Suction Cup Here As It Will Separate The Glass From The Black/White Framing That You're Actually Supposed To Pry Under. I Found When Using The Suction Cup, The Glass Came Up, But The Framing Stayed Stuck. If You're Replacing The Entire Display It's Not As Much Of A Problem, But If You're Installing Any Other Part Or A Custom Housing, You'll Notice Your Screen Has A Bit Of "Play" When Pressing Down.