Here's some incentive to get it installed... Run this with an argument of '*.txt'.

use Bio::Seq;
use Bio::SeqIO;

while(my $fname = shift) {
  open(INSEQ, "<$fname") or die $!;
  my $seq;
  ## Grab all the sequence in a single string
  while(<INSEQ>) {
      chomp;
      $seq .= $_;
  }
  close INSEQ;
  my $fname =~ s{\.txt}{}; # strip .txt

  ## Create a new Bio::Seq object with your sequence
  my $seqobj = Bio::Seq->new(-display_id => $fname,
                             -seq  => $seq
                             );

  ## Write it out to filename.fa
  my $outfile = $fname . ".fa";
  my $seqout = Bio::SeqIO->new(-format => 'fasta',
                               -file   => "> $outfile",
                               );
  $seqout->write_seq($seqobj);
}
[download]

Well, I didn't realize your input files were all newline free.. Should have read the question more closely.

In that case, Bioperl is even better...

use Bio::SeqIO;
while (my $fname = shift) {
   ## raw is one seq per line (no newlines)
   my $in  = Bio::SeqIO->new(-file => "$fname",
                            '-format' => 'raw');
   $fname =~ s{\.txt}{}' # strip .txt
   my $outfile = $fname . ".fa";
   my $out = Bio::SeqIO->new(-file => "> $outfile" ,
                           '-format' => 'fasta');
 
   ## Do the conversion
   while ( my $seq = $in->next_seq() ) {
       $seq->display_id($fname); # Add a name
       $out->write_seq($seq);
   }
}
[download]

Run it in the same way, with an argument of *.txt