Training for a class or type rating must be conducted by an ATO that has an approved SEP course or a DTO that has declared a training programme for such a course, it cannot be done by an independent FI in the manner that you suggest.
FCL.725 Requirements for the issue of class and type ratings
(a) Training course. An applicant for a class or type rating shall complete a training course at an ATO. An applicant for a non-high-performance single-engine piston class rating, a TMG class rating or a single-engine type rating for helicopters referred to in point DTO.GEN.110(a)(2)(c) of Annex VIII (Part-DTO) may complete the training course at a DTO. The type rating training course shall include the mandatory training elements for the relevant type as defined in the operational suitability data established in accordance with Annex I (Part-21) to Commission Regulation (EU) No 748/2012.
(b) Theoretical knowledge examination. The applicant for a class or type rating shall pass a theoretical knowledge examination organised by the ATO to demonstrate the level of theoretical knowledge required for the safe operation of the applicable aircraft class or type.