Read file 2 first: load it into a hash with the numeric ID's as the hash keys and the strings as the hash values.

Then, as you read through file 1, use a regex to match and capture the digits at the end of each line. If there's a hash element with that digit string as the hash key, replace the digits at the end of the line with the corresponding hash value, and print the result to a new file (or to STDOUT, and redirect that to a file).

Have you written any perl code for this yet? If not, now's the time to try.

(updated to fix second paragraph)