01.txt
>SR1.2
>SR1.3

02.txt
>SR1.1 HWI-ST
ATGCTGCT
TCGTCGAT
CTGATCAGCTAC
>SR1.2 HWI-ST0
TTTTGCTGCT
TCGTTGGG
CTTTATCAGCTAC
>SR1.3 HWI-ST0787
GGGGGCTGCT
AATCGTCGAT
AACTGATCAGCTAC

result
>SR1.2 HWI-ST0
TTTTGCTGCT
TCGTTGGG
CTTTATCAGCTAC
>SR1.3 HWI-ST0787
GGGGGCTGCT
AATCGTCGAT
AACTGATCAGCTAC



#!/usr/bin/perl -w
use strict;
open(IN1,"01.txt") || die "Cannot open this file";
my @lines1 = <IN1>;
open(IN2,"02.txt") || die "Cannot open this file";
my @lines2 = <IN2>;
my $i=0;
open(OUT,">out01") || die "Cannot open this file";
for my  $item1(@lines1){
        chomp $item1;
        my@tmp1=split(/\s+/, $item1);
for my  $item2(@lines2){
        chomp $item2;
        my @tmp2=split(/\s+/, $item2);
                if ($tmp1[0] eq $tmp2[0]){
                        print OUT $lines2[$i],"\n",$lines2[$i+1],$lines2[$i+2],$lines2[$i+3];
                        last;
                }
        $i++;
}
print OUT "\n";

}

close(IN1);
close(IN2);
close(OUT);