Your best bet is to cut off the side bars and bottom bar of a frame or 2 of the Langs. frame.
This will let them fit into a TBH. Then brush off some young nurse bees into the TBH on top
of these cut off frames. Put the new queen cage between the frames and you will have a new hive soon.
Be sure to tie the Langs frames onto the TB to extend their length before putting them in the new hive. If you
have a strong Langs hive now then you can brush off more young nurse bees into the TBH. This way they will
build new comb faster. If you have 2 deep then brush off as many nurse bees as you can. And don't forget to
feed them too.
This will let them fit into a TBH. Then brush off some young nurse bees into the TBH on top
of these cut off frames. Put the new queen cage between the frames and you will have a new hive soon.
Be sure to tie the Langs frames onto the TB to extend their length before putting them in the new hive. If you
have a strong Langs hive now then you can brush off more young nurse bees into the TBH. This way they will
build new comb faster. If you have 2 deep then brush off as many nurse bees as you can. And don't forget to
feed them too.