just tell it to go to the other planet. It's automatic.

Ah, thanks.

Well, I loaded up the game and tried to use the stabilizer by just directing the ship to the planet with the other stabilizer, but it just bypasses the stabilizer. Also the stabilizer doesn't have the graphic of the portal in its center. What am I missing?

Okay so I answered my own question. I scuttled all my stabilizers and rebuilt them. I see that it allows me to traverse two planets that have no phase lane. Is this the real point of them? I thought they would behave like some kind of teleportation device. My question is: if the planets already have a phase lane, is there a point to building a stabilizer at both?

And also, can the stabilizer work between solar systems or only within one at a time?

Phase stabilizer is a structure that, "as it says" stabilizes Phase space,  it is NOT a wormhole or teleportation device

phase stabilizers work wonders,  you can get from point to point, even if theres no phase lane   downside is that both planets need a stabilizer in order for it to work   

to make it work  once both the planets have a FINISHED stabilizer ships wil use an invisible phase lane  that exists between them until one of the stabilizers are destroyed.

Phase stabilizers do NOTfunction between star's  so you cannot go from STAR A: planet 1    to   STAR B: planet 2 the destination has to be in the same star system.

if you order to go from STAR A: planet 1    to   STAR B: planet 2 the ships will take the shortest route "even use stabilizers to get to the star the quickest

you can build as many stabilizers as you want until either recources / planets /planet slots are depleted

having 4 planets in a row named A B C and D

where ---- are phase lanes

A----B----C----D

going from planet A to B is simple   you do not need a PS

going from planet A to D takes 3 jumps  a PS on both planet A and D wil cut the 3 jump journey in a 1 jump journey

going from planet D to B takes 2 jumps  to cut that down to just 1 jump can be worth it if either D or B is a planet commonly visited by ships

overall  if you have low recources it is recommended getting a stabilizer on your factory planet A to the battlefront D  in just 1 jump your ships will arrive instead of 3

if you have enough recources,  getting a stabilizer on A B C and D ensures you are able to go form anywhere to everywhere in just 1 jump

Star to Star phase lanes

A----B----C----D----STAR1 - - - - - - - STAR2----E----F

it doesnt matter, even if u have a stabilizer on all avaible planets "A B C D E F"stabilzers do not function between stars,  you'll have to go from star 1 to star 2 first to get to either E or F

if you are on A to a journey to E  however your ships will Phase jump directly from A to D to Star1 to Star2 to E 

hope u bothered reading it,  this is pretty much how the phase stabilizer works

it also gives the ability Returning Armada "RA"  if you researched it "manually activate on every Phase Stabilizer as soon as the research is done"  takes about 20 seconds for ships to arrive tough

S_o_L

The artificial phase lane network can be made even more efficient if you can get to the Tier 7 tech Enhanced Tunneling, which increases phase jump speed in phase lanes created by Stabilizers by 20%/40% (both levels is needed for RA anyway).

A Phase Stabilizer network is also required to use the Antorak Marauder's ultimate ability, Stabilize Phase Space, which creates a temporary phase stabilizer (which explains the circular apparatus near the Marauder's engines) for 75 seconds.