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Yes, the migration will start back over when you connect the computers again. One suggestion that I can give is to have both computers connected to your internet via an ethernet cable. The files will not be double transferred and to try and prevent the hanging up at the end, try the ethernet trick.
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Your issue is actually a "common" one but it does not have a definite resolution to fix the issue. Where some issues were fixed by just running the migration again and others were fixed by performing the steps that I gave you; there were others that never had a solution to the problem.
I would suggest taking the computers to a local repair shop or having a local tech come to your issue to view the migration process to make sure there is nothing wrong.