Yes. And according to GR, both viewpoints are valid.
At any given instant, it may be taken to be moving or not as one pleases. There is no inertial frame in which it is continuously at rest. But that's not the same thing as saying that it is always moving.
About the OP, I got a shortcut answer.
Let's get practical! The speed of light one way is impossible to measure, and the OP assumes that it is. In real life, we will never have to solve that kind of problem, because we will never face it, so it is no use to study it.
Separate names with a comma.