It would help if you include the non-working code that you have so far, with descriptions of error messages that you get.

If all you need is appending messages to a file, you don't need Perl to do that. A simple mail alias defined in /etc/aliases (or the corresponding NIS/NIS+ table, if you use that) or in the user's .forward file will suffice, using the following format:

"|/bin/cat > /file/to/append.txt"
[download]

or simply

"/file/to/append.txt"
[download]

Remember that if the alias is defined in /etc/aliases or other system table, the program gets executed as root (daemon in some systems?), so you need to make sure the file has correct permissions. You could also pipe it to a setuid/setgid program, and then make sure the file again has appropriate permissions.

If you need to do some pre-processing on the message before appending it, then you need to pipe it to a program, and that is where Perl could be useful. Take a look at the Mail::Internet package for mail manipulation utilities. Assuming your program leaves the (possibly) modified message on STDOUT, you need an alias like this:

"|/your/program.pl > /file/to/append.txt"
[download]

in which case again the file gets written by root/daemon. If your program open the file for writing internally, then you only need

"|/your/program.pl"
[download]

and make sure the setuid/setgid settings of your program match the permissions on the file.