If the qualification you have completed with The FA is a UEFA qualification (UEFA A, B or Pro-Licence) you will need to complete a cross-border form (attached) to request permission to do so. Please note permission is not guaranteed. It is a requirement of the UEFA as set-out in the UEFA Coaching Convention to gain this permission.
If your qualification isn't UEFA Accredited (Level 1 or 2, Playmaker or the Introduction to Coaching Football) you do not need permission from The FA in order to take a qualification with a different association.