How to link a reared queen to a colony
A queen created within a rearing run keeps a reference to the run itself and to her parent queens — mother and father. Those references are what the printable “Queen pedigree” is later built from.
From there the queen is introduced the usual way — “Attach queen” on the hive card, or “Add” on the queen’s own record; see Queens.
Once she is in, the link is visible from both ends: her pedigree shows who she came from, and the rearing card shows which queens came out of it. Do fill in the parent colony and queen on the rearing run — without them the pedigree simply stops there.
If you detach the hive from a rearing run, the app warns you that the hive will be detached, the run and its data will be kept, and the change applies when you save. The run itself is not going anywhere — detaching only changes which hive it is tied to.