In my understanding when it comes to SP type or weight is not relevant, but a TRI can do MP helicopter type ratings where as this privilege is not mentioned for the FI. Relevant bits of UK Part-FCL:
FCL.905.FI FI - Privileges and Conditions The privileges of FIs are to conduct flight instruction for the issue, revalidation or renewal of:
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(b) class and type ratings for single-pilot aircraft, except for single-pilot high-performance complex aeroplanes;
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(i) single-pilot multi-engine class or type ratings, except for single-pilot high-performance complex aeroplanes, provided that they meet the following conditions:
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(2) in the case of helicopters, comply with points FCL.910.TRI(c)(1) and FCL.915.TRI(d)(2);
and the referenced points:
FCL.910.TRI TRI - Restricted Privileges
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(c) TRIs for helicopters — TRI(H)
(1) The privileges of TRIs(H) are restricted to the type of helicopter in which the assessment of competence for the issue of the TRI certificate was taken. Unless otherwise determined in the OSD, the privileges of the TRIs shall be extended to further types if TRIs have:
(i) completed the relevant parts of the technical training and flight instruction parts of the TRI course;
(ii) completed within the 12 months preceding the date of application, at least 10 hours on the applicable helicopter type, of which a maximum of 5 hours may be completed in an FFS or FTD 2/3; and
(iii) passed the relevant sections of the assessment of competence in accordance with point FCL.935 in order to demonstrate to an FIE or a TRE qualified in accordance with Subpart K of this Annex their ability to instruct a pilot to the level required for the issue of a type rating, including pre-flight, post-flight and theoretical knowledge instruction.
and
FCL.915.TRI TRI - Prerequisites
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(d) for TRI(H):
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(2) for a TRI(H) certificate for single-pilot multi-engine helicopters, have completed 500 hours as pilot of helicopters, including 100 hours as PIC on single-pilot multiengine helicopters;
I hope someone who actually knows about this can confirm or deny my understanding though...