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Probably. I had a Chase Sapphire card with 6800 CL for 4 months. then I got a Freedom with 1800. I though that was too low so they let me move 1800 from sapphire to freedom. Both accounts where young accounts. This was in mid/end 2014
If you want to transfer the entire amount over you have to have a $0 balance and not used the card for 30 days. Otherwise you can transfer all but $500 and have to keep the card open
I would call them and work it out. They are more than willing to work with you.
As metioned, no activity and paid off in full balance is key