Let's say in another words: You have a Perl program, "A", runs with PID 32237. A forks another process, "B", with PID 31238. So, B is the child process of A. B then exec's another program, "C". Now, C is replacing the process B and using B's PID which is 31238. The original parent, which is "A", needs to know the PID of C. That is 31238. Is it correct?

Consider this:

# /tmp/child-child.pl
print "I'm exec'd: $$\n";
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Then in the main program (/tmp/main.pl):

#!/usr/bin/perl

use strict;
use warnings;

print "I'm parent ($0): $$\n";
my $child = fork;
defined $child or die "Can't fork: $!\n";

unless ($child) {
    print "I'm child ($0): $$\n";
    exec $^X, '/tmp/child-child.pl';
}
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The output is:

$ perl /tmp/main.pl
I'm parent (/tmp/main.pl): 12499
I'm child (/tmp/main.pl): 12500
I'm exec'd (/tmp/child-child.pl): 12500
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Update: fixed typo