Phase Stabilizers can be a little frustrating. There's about a five minute delay from when it's finished building to when it will actually work.
When they do work, however, you should be able to jump directly from one planet to any other planet within the star system provided you have either:
a. own a phase stabilizer there
b. Have a level 6 Marauder capital ship at a planet that acts as a phase gate
c. Have a starbase acting as a phase gate
d. recently shot the planet with a Kotsura Cannon Blast (Tier 8 Military super structure, it's to the far right in the weaopns tech tree).
