G'day Bioinfocoder,

Welcome to the Monastery.

Here's 'pm_1149165_zip_merge.pl', which appears to do what you want.

#!/usr/bin/env perl

use strict;
use warnings;
use autodie qw{:all};

open my $gz_pipe, '|-', 'gzip >> pm_1149165_all.gz';

while (<>) {
    open my $zcat_pipe, '-|', "zcat $_";
    print $gz_pipe $_ while <$zcat_pipe>;
}
[download]

Here's a sample run (with minimal test data):

$ zcat pm_1149165_1.gz
q
w
e
$ zcat pm_1149165_2.gz
a
s
d
$ zcat pm_1149165_3.gz
z
x
c
$ cat pm_1149165_list
pm_1149165_1.gz
pm_1149165_2.gz
pm_1149165_3.gz
$ ls -l pm_1149165_all.gz
ls: pm_1149165_all.gz: No such file or directory
$ pm_1149165_zip_merge.pl pm_1149165_list
$ ls -l pm_1149165_all.gz
-rw-r--r--  1 ken  staff  38  3 Dec 11:44 pm_1149165_all.gz
$ zcat pm_1149165_all.gz
q
w
e
a
s
d
z
x
c
[download]

I'll leave you to add in argument checking, usage message, and similar niceties.