Migrating solid state drive to new machine
Assuming the drive fits, you should be able to insert the drive in the new Mac and see if the OS is capable of booting. I would make a good backup of the contents of the drive before starting if you can.

If you wanted to be safe, you could use Internet Recovery to install the OS on op of the drive or even wipe it clean and migrate things at a later date. 

The drive will either physically fit and be a SATA device or not. The data part of things will be driven by your backup situation and comfort with spending time testing the OS or running a new install to ensure the drivers and OS are proper for the new hardware.

The symptom of three beeps means that the machine has not even completed the POST where RAM is checked, so you will want to first resolve whatever hardware issue is preventing the machine from completing the power on self test (POST).