I think it isn't quite clear what it is you were asking so that may have caused a little confusion.
Your image Support Ticket Title "Can I had my new lap top to my current account ? Or do I have to purchase another plan ?"
I believe this had been interpreted as, Can I had add my new lap top to my current account, as in add another system to your existing one (not transfer to new system) and the answer would be no as it would be being used on two systems.
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So I think it is confusion on how many systems this would be on, you can safely do as I have suggested transfer the license to the new system and dispose of the dead one (removing avast if possible, so it can't be used).