Not the case I'm afraid. An FI with only a PPL - hence without CPL TK passes - is only permitted to teach LAPL students
Actually, there are a number of PPL FIs without CPL knowledge who can teach the PPL. All those who were grandfathered in the past and since the implementation of EASA all those who held a FI in the past that has expired, but who did not have CPL level knowledge may now renew their FI and are permitted to teach the PPL on the basis of grandfather rights. It is only those who have acquired a FI since EASA implementation that are restricted to teaching the LAPL if they don't have CPL TK knowledge.