The last frame position of your stabilize obviously has to match the first frame of your non-stabilized portion of your shot.
If you are using Mocha Pro's stabilize module, there is a cool feature called 'Fixed Frame List" where you can reset any given frame to have no stabilization applied. This is a great way to stabilize general motion and to reduce high-frequency jitters, built leave original motion.
In your case, if you set the fixed frame on the last frame of your stabilize render in Mocha Pro it would be the solution.
If using Mocha AE, on the last frame you would reset all transformation keyframes, so it matches the incoming portion of the shot.