Satellite in orbit in front of and behind the Moon Would it be possible to put a satellite into the same orbit as the Moon, but far enough ahead or behind the Moon to remain in place?

Has this ever been done in practice?
Yes. Trojan orbits (60° before or after the Moon) are even stable in most cases. These points are called the L₄ and L₅ points, which are two of the five Lagrangian points.

These orbits are mostly impractical (nothing is there).

Today the most known is the Chinese Queqiao satellite, which is a communication relay to their probe on the far side of the Moon. Instead of using L₄ or L₅, Queqiao is in a halo orbit around another Lagrangian point; Earth-Moon L₂.