As noted, on an airplane without an AFM (Approved Flight Manual) the POH does not need no be on-board, only a placard with the operating limitations. The cutoff for the AFM requirement are individual aircraft that had their first flight after 1 March 1979.

As the owner/operator of an early 1979 build aircraft that does not have an AFM, I’ve had this discussion with maintenance/airworthiness inspectors so frequently that I keep a printout of 14 cfr 21.5 in my POH.

https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C...