No, the mailing addresses do not need to match on an Automated Customer Account Transfer Service (ACATS).
Does my mailing address need to match on an ACATS?
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How do I transfer cash from another brokerage account to IBKR?
How do I transfer my existing IRA to Interactive Brokers?
Can I transfer international shares with an existing margin loan from another broker to my IBAU account?
What address is my check withdrawal mailed to?