If I've done the original EICR, and the remedial works, I will usually issue a revised EICR (with a different reference number, and added date(s), to the original) with the certification - this is very easy for me to do, and just makes things simpler for everyone.
If I'm doing remedial work for an EICR done by others, I make a statement on the invoice (or covering email) stating that the works done rectify the (specific, referenced) observations on the EICR "done by others" (include their reference number)... as well as relevant certs done for the work, obviously.