ICAO Doc 4444 mentions to input AFIL in the departure field of flight plan if it has been filed in the air. What is an Air-Filed flight plan? Can aircraft crew file a flight plan in-flight? If yes what are the equipment that support filing flight plans when in flight?
It is quite easy in the US but it depends on controller workload. You need to be in a plane equipped for IFR flight and you need to be IFR current.... to legally use a filed IFR flight plan.
If the controller is too busy they will make you file through a flight service station. This can also be done in flight but requires you to change frequencies, reach the FSS, wait your turn, and then file. The FSS puts you in the system. Then you call ATC back and open your plan  -or- open with the FSS.
If the controller has time, they will file you on frequency.
To answer your question directly, the equipment enabling a pilot to file a flightplan while in the air is a radio. It is rarely needed, but air traffic control can file a flightplan submitted by a pilot over the radio. An air-filed flightplan is just that - a flightplan filed (via ATC) while an aircraft is in the air. It is a complete flightplan that lets you do all the same things a flightplan filed before departure does.
Note that landing at a different destination than the one filed in your flightplan does not require a pilot to file a flightplan from the air - diversions are handled by direct ATC coordination, without filing a new flightplan.