Straight from the horse's mouth
I have bolded my commentary
§ 61.65 Instrument rating requirements.
(a) General. A person who applies for an instrument rating must:
(1) Hold at least a private pilot certificate with an airplane, helicopter, or powered-lift rating appropriate to the instrument rating sought; If you are JAA PPL, this is an easy PAPERWORK converstion
(2) Be able to read, speak, write, and understand the English language. If the applicant is unable to meet any of these requirements due to a medical condition, the Administrator may place such operating limitations on the applicant's pilot certificate as are necessary for the safe operation of the aircraft;
(3) Receive and log ground training from an authorized instructor or accomplish a home-study course of training on the aeronautical knowledge areas of paragraph (b) of this section that apply to the instrument rating sought;
(4) Receive a logbook or training record endorsement from an authorized instructor certifying that the person is prepared to take the required knowledge test;
(5) Receive and log training on the areas of operation of paragraph (c) of this section from an authorized instructor in an aircraft, flight simulator, or flight training device that represents an airplane, helicopter, or powered-lift appropriate to the instrument rating sought;
(6) Receive a logbook or training record endorsement from an authorized instructor certifying that the person is prepared to take the required practical test;
(7) Pass the required knowledge test on the aeronautical knowledge areas of paragraph (b) of this section; however, an applicant is not required to take another knowledge test when that person already holds an instrument rating; and
(8) Pass the required practical test on the areas of operation in paragraph (c) of this section in—
(i) An airplane, ......
(b) Aeronautical knowledge. A person who applies for an instrument rating must have received and logged ground training from an authorized instructor or accomplished a home-study course on the following aeronautical knowledge areas that apply to the instrument rating sought:
(1) Federal Aviation Regulations of this chapter that apply to flight operations under IFR;
(2) ......
(c) Flight proficiency. A person who applies for an instrument rating must receive and log training from an authorized instructor in an aircraft, or in a flight simulator or flight training device, in accordance with paragraph (e) of this section, that includes the following areas of operation:
(1) Preflight preparation;
(2) .......
(d) Aeronautical experience for the instrument-airplane rating. A person who applies for an instrument-airplane rating must have logged:
(1) Fifty hours of cross country flight time as pilot in command, of which 10 hours must have been in an airplane; and This means 50 hours of PIC flight time flying from point A to point B with a landing at point B
(2) Forty hours of actual or simulated instrument time in the areas of operation listed in paragraph (c) of this section, of which 15 hours must have been received from an authorized instructor who holds an instrument-airplane rating, and the instrument time includes:
(i) Three hours of instrument flight training from an authorized instructor in an airplane that is appropriate to the instrument-airplane rating within 2 calendar months before the date of the practical test; and
(ii) Instrument flight training on cross country flight procedures, including one cross country flight in an airplane with an authorized instructor, that is performed under instrument flight rules, when a flight plan has been filed with an air traffic control facility, and that involves—
(A) A flight of 250 nautical miles along airways or by directed routing from an air traffic control facility; This must be within the 15 hours with CFII
(B) An instrument approach at each airport; and
(C) Three different kinds of approaches with the use of navigation systems........
So the MINIMUM amount of flying time to get a FAA IR if you have a JAA IR is 15 hours + check ride.