An ME IR(H) only needs a TRI & TRE for the conversion. An SE IR(H) holder also needs an IRI, who might not necessarily be 'on staff'
From FCL.905.TRI:
The privileges of a TRI are to instruct for:
(a) [...]
(b) [...]
(c) [...]
(d) [...]
(e) in the case of the TRI for helicopters:
(1) the issue, revalidation and renewal of helicopter type ratings;
(2) MCC training, provided he/she holds a multi-pilot helicopter type rating;
(3) the extension of the single-engine IR(H) to multi-engine IR(H);