Not that simple, there is a process of validating your current license. The FAA have to request your "paperwork" from the CAA, and then go through the process of making sure you are who you say you are and have the flight experience you say you do etc. Then you have to get TSA clearance to undergo flight training for a FAA certificate. Before you start this process, contact FSI, and get confirmation that you will indeed be able to do the checkride on a recurrent. It is not always the case. The process can take a couple of months, so start early before your recurrent.