During the Apollo missions, including the iconic Apollo 11 moon landing, the lunar module's ascent stage (which carried the astronauts back to the command module in lunar orbit) was not filmed from the moon's surface. The footage we commonly see of the lunar module taking off from the moon is captured by a camera mounted on the outside of the lunar module itself.
The lunar module had a 16mm movie camera called the "Data Acquisition Camera" (DAC) mounted on its instrument panel. The astronauts, before leaving the lunar surface, would set up the DAC to capture the ascent. The DAC was remotely triggered from inside the lunar module by astronaut Buzz Aldrin using a cable release.
The footage captured by the DAC showed the lunar module's ascent stage rising from the moon's surface, its separation from the descent stage, and the rendezvous with the command module in lunar orbit. This camera was specifically designed for engineering and documentation purposes to provide valuable data and record important events during the mission.
It's important to note that the footage we see of the lunar module taking off and rejoining the command module is from the DAC camera, not from a separate camera placed on the moon's surface.