This comes up every year in that the beekeeper has over winter decided to invest in a “better” hive, and they may be right though in my view if they are not going poly they ain’t but that’s another matter.
So………… how to.
Lets start by assuming the hive footprint is the same, or in plain language the one box fits the other box.
Some people advocate moving them when they are weak as it is easier, but I prefer to do it when they are strong, at least 8 frames of brood, note brood please as it is the best guide to strength. Bees covering 8 frames which contain 3 frames of brood are nowhere near as strong as a colony supporting a brood nest of 8 frames of brood. Chalk and cheese in fact.
So when my colony is strong enough I put the new box on top and when the queen is up there I put in a queen excluder. Assuming she is up there then 24 days later (to allow for drone brood to hatch) the job is completed.
If there are no eggs visible four days after putting in the excluder then remove it to let her up. Queens always want to go up by the way, a useful trait at times and at others a pest.
But says you my hives do not fit each other.
My method is to cut some sheet material to fit the larger box, with a hole in it to fit the smaller box. Put the new box on top using the adapter sheet and off you go as above.
When transferring a nucleus move the combs over in the same order but go hive wall, foundation frame, nucleus, then foundation to fill the box out.
It’s truly not difficult if you get the bees to do the work for you, and on that note they will if the weather is a bit adverse very much appreciate a feed of 1:1 syrup to help them draw out their new combs.