Not impossible, but a bit of work required
What Bert says is exactly correct. I had a SA ATP (still do) and decided to get an FAA ATP. In short I did not even bother to try "convert" my SA licence. The FAA will recognise your experience (documented in your logbook) so all you need to do is write the knowledge exam (1 very easy exam) and take a check ride in an aircraft. You can do an ATP test in a C172 for example and this will give you a FAA ATP restricted to single engine land airplanes. If you want an FAA ATP that allows you to fly both single and multi-engine planes, then you must take two checkrides, one in a single and one in a multi-engine plane.
You can accomplish an FAA ATP in about 3 days if you have the hours required as laid out in the FARs.
Hope it offers some help.