B737-700
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Time Pressure; Communication Breakdown; Other / Unknown
Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Hazardous Material Violation; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Overcame Equipment Problem
Human Factors
Operations notified me of two aircraft batteries on the aircraft.  We waited for the NOTAC [Notice to Captain] to arrive. I filled out one form and kept the other one with the required paperwork.  Dispatch notified us enroute to make sure we knew about the batteries. We then made a note under the remarks section of the release stating HAZMAT on flight.
We were delayed out of ZZZ because we needed the correct paperwork for HAZMAT that was loaded. Once we received it; and the Captain reviewed it and signed it; we were on our way. Once airborne; Dispatch sent us a message advising us it needed to be on the release and to fill out a report.
B737-700 flight crew reported Dispatch notified them enroute of missing Hazmat information on Final Flight Release documentation.