$ cat forked.pl
#!/usr/bin/perl
use strict;
use warnings;
open FH, ">forked.dat" or die $!;
print FH "forked $$\n";
close FH;
print STDERR "This should not appear ($$)\n";

$ perl -wle'
if (my $pid = fork()) {
  print "parent $$ forked $pid";
}
elsif (defined $pid) {
  close STDERR;
  exec qw(perl forked.pl);
}
'
parent 29747 forked 29748

$ cat forked.dat 
forked 29748