I just did an EASA ATPL with G-V rating to an FAA ATP with the G-V rating (I already held an FAA Commercial with I/R and Multi). I had to do the following ...
Pass the written
Get the TSA approval
Get the CAA to verify my EASA licence to the FAA
Pass the G-V checkride
All pretty straightforward as has been said but, get the written done before the end of July or it all changes!
Happy landings
3 Point