Considering you use the word "split" in the title of your post, it's funny you aren't using split to process the text.

our $all_text = join "", <ARGV>; # files, STDIN, etc.

our $key_phrase = "This is "; # should not be hard-coded
our $base_name  = "UserA_";
our $ext        = ".txt";

our @bits = split m/\Q$key_phrase\E/, $all_text;
# if line 1 data includes the key phrase, element 1 will be empty:
shift @bits if $all_text =~ m/^\Q$key_phrase\E/;
                                                  
my $count = 1;
foreach my $bit (@bits) {
  # suggest padding the index number so files sort correctly
  my $filename = sprintf "%s%2.2d%s", $base_name, $count++, $ext;

  open FILE, ">", $filename
    or die "Could not write to \"$filename\": $!\n";
  print FILE "$key_phrase$bit"; # put back the what split() excised
  close FILE;
}
[download]

This solution assumes that you can read all the data into memory, of course, but unless it's a million lines or an ongoing TCP/IP connection or something, I rarely have issues with that.