The examiner has to have 'ATPL-LST' on his examiner authority. Most FSI examiners do not have this authority.
If you have a UK CAA national licence then it can go on there and you do not need an ATPL skills test. You can then convert the UK CAA national ATPL to a JAA ATPL. You have to pay a fee of course.
If you only have a JAA licence then yes you must do a ATPL skills test which can be a pre-arranged part of the type rating checkride. You need the SRG 1187 form signed and the ATPL skills test box ticked by the examiner.
However, it is not FSI responsibility to work that out, you have to ask them for it when you arrange the rating. It is on all the forms you fill in when requesting the training.
Oh and one other thing; the UK CAA will no longer give one-off ATPL-LST authority to examiners like they used to.