Moving the queen

[AceCadet]

Just tape the tubes together, pop airholes in it, and let her move at her own pace. Or even use some tubing with air holes obviously. And just leave her to do her thing. Its already going to be stressful if she has no workers so the less disruptions the better. If she finds the humidity in the new tube more appealing she will move in time. Hope this helps. And if you use tape try to rid some of the stickyness on a piece of fabric or whatevs. So your queen doesnt get stuck to it. Happy Ant Keeping!

[Serafine]

If the queen is small enough you can put both test tubes into a container (outworld) and connect both of them with a drinking straw (just gently drive it though the cotton). That way you don't have to fully remove the cotton and the whole environment in the tubes will remain more stable.
But be prepared for some wait, Lasius niger has a reputation of being especially stubborn when it comes to moving anywhere new.