I guess that permission to conduct IR(A) includes the permission to conduct BIFM no?
No. To teach for a CPL there is no requirement for the FI to have IRI privileges. To teach for the IR including the PIFM the FI must have IRI privileges. So unless you have a CCC for the PIFM or hold a CPL there is no credit towards the Modular IR. Whilst IFT completed by a FI qualified to teach for the IR may be counted towards the CBMIR, then IFT conducted by a CPL FI who is not IRI qualified would have no credit.