my $count = 1;

my $outfile;
while (<DATA>) {
    if ( my($regex) = /This is/g) {
        close $outfile if $outfile;
        open $outfile, '>', "UserA$1_$count.txt"
            or die "could not open 'UserA$regex.txt' $!";
			$count++;
    
}
    print {$outfile} $_;

}

__DATA__
This is line 1 from text 1
another line here which should be included in the text file with the above line.
This is line 2 from text 1
This is line 3 from text 1	
This is line 1 from text 2
This is line 2 from text 2
another line here which should be included in the text file with the above line.
This is line 3 from text 2