There isn't a requirement for the Flight Operations Manual to be approved by the POI.

FOM's are covered under FSIMS 8900.1, VOLUME 3 GENERAL TECHNICAL ADMINISTRATION - CHAPTER 32 MANUALS, PROCEDURES, AND CHECKLISTS FOR 14 CFR PARTS 91K, 121, 125, AND 135 - Section 4 General Operations Manuals for Parts 121 and 135.

Per 8900.1, only the Weight and Balance procedures and Company Aircraft Operating Manual Limitations, Procedures and Performance sections are required to be approved.

This is why Boeing divides the FCOM into Volume 1 and Volume 2. Volume 1 requires POI approval while Volume 2 is accepted by the POI.