Select the parts you want to move. Then on the Home tab in the Modify section is a Transfer command.
But will it keep the assembly relationships? For example, in his picture, he also has an "ASM2" file. What if one of the original parts had a relationship with that subassembly (or parts in it), then now when all those parts are transfered to a new subassembly, will the relationships still hold?
I'm asking because I tried to replace a part in an assembly with a subassembly (which contained that part), and all my relationships failed/suppressed and now I need to manually update them all!
As you want to move all the parts I would just delete Assy1.asm from TopAssy.asm then Save As (or Rev Manager copy) the TopAssy.asm to Assy1.asm.
Re-open TopAssy.asm, delete the parts and re-attach Assy1.asm
All your relationships will then be kept.
The only thing to take care with is the links on Frame3,Part9 & Part12.