"nothing ever moves" does not mean that no blocks in the block universe are related in such a way that we can reasonably say the same object is in both. and if the same object is in two or more blocks of the universe, which are different times, then it exists at different times, or in other words travels through time. this doesn't prove traveling back in time, or skipping forward in time is possible, but the concept does make sense in a block universe, and the standard time travel via time passing still works fine.

But +1 for quoting Popper.