Firstly, yes it is possible to write to a local file. I tried your program and it worked creating menu.txt.

If the file didn't get created then it is probably being created somewhere else. Put a

use Cwd;
print cwd();
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Into your program to see where it thinks the current directory is, then look there for menu.txt

Secondly - check the version of perl between your local machine and the remote machine.

perl -V
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Will tell you, or if you don't have shell access just run that from a system command.

If it is < perl 5.6 then use diagnostics won't work which is a possibly explanation.