Even during “normal” times it takes about four months for the IRS to process an amended return. During the pandemic and due to the severe backlog at the IRS it is taking much longer—six months or more for many amended returns. Do not expect quick results from amending. When the IRS issues a refund for an amended return it will be by check. They do not make direct deposits for refunds for amended returns. You can watch for information here:
https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1
I am moving in 2 months and if the processing is not finished can I then update my mailing address as it would be different from my address on my amended return .
Yes you can and should update your mailing address and also make sure you have your mail forwarded by the post office.
CHANGE OF ADDRESS
https://www.irs.gov/faqs/irs-procedures/address-changes/address-changes
Also when you move you should have the post office forward your mail.