There is, of course, no such thing as a 'frozen' ATPL - the term is shorthand for a CPL + MEIR + MCC + ATPL Theory. You will, therefore, need to take the relevant courses and pass the relevant exams/flight tests to achieve all of these qialifications. Some credit may be available for the FAA qualifications that you already hold, depending on your experience.
MEDICAL - Before commencing any training it would be wise to ensure that you are able to obtain a JAA Class 1 medical, the requirements for which differ somewhat from the FAA equivalent.
ATPL Theory - You will have to complete an approved course of training and pass the 14 theoretical knowledge examinations at ATPL level. You should aim to do this before commencing the flying training.
CPL - Assuming that you meet the experience requirements for isue of a JAA CPL(A), you will need to complete, at an approved FTO, sufficient flight training to pass the CPL Skill Test. The amount of training will be at the discretion of the Head of Training of the FTO. If you select the UK as your state of licence issue, you will also need to obtain a Flight Radio Telephony Operator's Licence - other states have different RT licensing requirements.
MEP - If you have at least 100 hours experience as a pilot in MEP aeroplanes, no training is required before attempting the Skill Test. If you do not meet the experience requirement, you will have to undergo training at the discretion of the Head of Training of an approved FTO
IR - You will need to complete an approved course of training at an FTO and pass the IR Skill Test. The amount of training (nominally 50 hours) may be reduced, again at the discretion of the Head of Training, to not less than 15 hours.
MCC - You will have to complete an approved course of MCC training.