I'm sorry but if you only hold an FAA CPL then you are NOT exempt from the groundschool requirement unless they are just going for the CPL(A) exams.
Ie, within Lasors, Section D, Page 8, under the heading "Non-JAA CPL(A) Licence":
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The holder of a valid (or non-expiring) CPL(A) issued in accordance with ICAO Annex 1 by a non-JAA State may be issued with a JAA CPL(A) providing the experience requirements of JAR-FCL 1.555(b) and (c) have been met. Applicants must:
Hold a valid JAR-FCL Class 1 Medical Certificate
Undertake CPL(A) theoretical knowledge instruction as determined by the Head of Training of an approved training provider and pass ALL of the JAR-FCL theoretical knowledge examinations at CPL(A) level. Applicants who wish to attempt examinations at a higher level (ie, ATPL(A) level) must undertake the full 650 hour course approved theoretical knowledge instruction and pass ALL of the JAR-FCL theoretical knowledge examinations at ATPL(A) level.
Blah blah blah...
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If you hold an FAA ATPL and haven't met the high experience requirements (ie, 500 hours Multi Crew etc) then you will find in Lasors, also in Section D on Page 8, under the heading "Non-JAA ATPL(A) Holders":
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The holder can of a valid (or non-expiring) ICAO ATPL(A) who does not meet the experience requirements for the grant of a JAR-FCL ATPL(A) as detailed in Section G1.5, can still apply for a JAA-FCL CPL(A)/IR. Applicants must:
Hold a valid JAR-FCL Class 1 Medical Certificate.
Undertake CPL(A) and IR(A) theoretical knowledge instruction as determined by the Head of Training of an approved training provider, and pass ALL of the JAR-FCL theoretical knowledge at CPL(A) and IR level. Applicants who wish to attempt examinations at a higher level (i.e. ATPL(A)) must undertake the full 650 hour course of approved theoretical knowledge instruction and pass ALL of the JAR-FCL theoretical knowledge examinations at ATPL(A) level.
Blah blah blah...
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So it looks like unless you have the experience on multi crew aircraft then you'll have to undertake the 650 hour course and pass all of the 14 exams at ATPL(A) level. You couldn't hold an FAA ATPL and just do the JAA CPL and IR exams as that will not give you the ATPL credits at JAA, thus you wouldn't hold a JAA "frozen" ATPL.