howto migrate jQuery 1.6 (!) AJAX requests to work with jQuery 2.0

howto migrate jQuery 1.6 (!) AJAX requests to work with jQuery 2.0

Dear all,
sorry for this (probably sounding stupid) question, but I have to migrate an existing application (which was developed by someone else years ago) from jQuery 1.6.2 (I know...) to a recent version (let's say 2.2.0).
Whenever I use any version of 2.x jQuery the application breaks, however it seems (at least partitially) to work with jQuery 1.12.0.

I do positively know the problem is with the usage of AJAX requests, so I hope someone could guide me towards a kind " howto migrate jQuery 1.9 AJAX requests to work with jQuery 2.0 " documentation (or some useful test-utilities) to help finding the flaw...

I dont need a "fully developed solution", but just some general guidance... (this is why I do not post any example code yet).

Hope my question attracts some of you "genious" to give me a starting-point...
kind regards
Ruediger