use strict;
use warnings;

# read file 1 into hash, don't forget to chomp; 
# left as exercise
# result should look like this:
my %file1 = (
    '>SR1.2' => 1,
    '>SR1.3' => 1,
    );

# loop over file two
while(<DATA>){
    next unless /^(>.*?)\s/ and exists $file1{$1};
    print $_.<DATA>.<DATA>.<DATA>;
}

__DATA__
>SR1.1 HWI-ST
ATGCTGCT
TCGTCGAT
CTGATCAGCTAC
>SR1.2 HWI-ST0
TTTTGCTGCT
TCGTTGGG
CTTTATCAGCTAC
>SR1.3 HWI-ST0787
GGGGGCTGCT
AATCGTCGAT
AACTGATCAGCTAC
>SR1.4 HWI-ST0787
GGGGGCTGCT
AATCGTCGAT
AACTGATCAGCTAC