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I'm probably wrong, but I say v=c.

In the reference frame of the ship, the star is 4.5 light-years away and it is approaching you at some velocity v. If it takes 4.5 light-years to get to you, then it is approaching you at a velocity of c. The clocks outside the reference frame of the ship are going slower. In fact, they are stopped when v=c.

Using the Lorentz equations I alway have one more unknown than I have equations.