Satellite in orbit in front of and behind the Moon
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.