What type of cichlid?
If they are not fertilized,don't move them.It's highly doubtful the male will finish the process once interrupted.
It would also be unlikely (but not impossible) that the parents would care for the eggs after all the commotion of moving everyone,and more likely that they would eat them.
The best bet at the moment is to leave everyone in place and let it play out.They spawned ... they will spawn again.Now that you know that,you can set the other tank up specifically for that if that's what you want.
For info though... if you submerge a container to move whatever the eggs are laid on,then submerge it in the other tank,they will never "see" air exposure.
Also,the eggs should have been fertilized by the male immediately upon laying.If they appear infertile after a couple of hours (which is how long it takes some cichlid eggs to change color) then they are infertile ... period.Also,in some species,two females will go through all the motions up to,and including,laying eggs.
So it is best to let this time play out to see what's what.
