Air carrier Dispatcher reported discovering the flight crew copy of the NOTOC after aircraft departure. The Dispatcher contacted the flight crew and reviewed the NOTOC in flight.

Narrative

Captain called to provide fuel slip at XA:18. At that time; no NOTOC (Dangerous Goods Form) for ZZZ-ZZZ1 had been received via email. Aircraft pushed out at XA:45 and was off at XB:01. I did not receive any further phone calls from the Captain; so I assumed that there was no NOTOC. Captain Called with Out Off Fuel and ETA times like normal at XB:16. I scanned my email a few minutes later and discovered that the attached NOTOC was sent via email at XA:30. I immediately attempted to reach the aircraft via Commercial Radio to confirm that the NOTOC was on board and that the crew had reviewed the information so that they knew about the hazardous materials they were carrying on board.I scanned my email after the initial radio call. I discovered the NOTOC. Delay in email from Company with NOTOC prior to departure. Also; cargo captains tend to depart early. While the Crew did in fact have the NOTOC on board; it is not clear from the radio call that they had reviewed it prior to departure. My immediate reaction was to contact the crew to make sure the NOTOC had been reviewed and was on board the aircraft. I reached out to commercial radio at XB:35z. I was connected with the crew at XB:42. The crew had the NOTOC on board and we reviewed it via the radio call.Send the NOTOC earlier. Have captains check paperwork thoroughly and call dispatch to review all NOTOCs if they are discovered in the paperwork so that they can be reviewed.