How do you write a letter to the IRS to explain about a different mailing address from home address in an amended return? Thank you!

See https://www.irs.gov/taxtopics/tc157

change the address on the amended return to your current one. if it's already sent in file form 8822 with the iRS

also file change of address with the USPS. 

https://www.irs.gov/pub/irs-pdf/f8822.pdf