If you use the 3rd arg to split, you shouldn't need to worry about recombining the line. Also, your code doesn't print anything to OUTFILE, it always prints to STDOUT.

#!/usr/bin/perl 

while ($line = <>){
    my ($file, $record) = split /\|/, $line, 2;
    if ( open(OUTFILE, ">>$file") ) {
        print OUTFILE $record;
    }
    else { 
        die("cannot open $record[0]");
    }

}
[download]

Some stylistic tips: You can use the -n switch to perl to get an implicit while(<>){} loop around your code, and you can use the short-cut nature of or to simplify your conditional:

#!/usr/bin/perl -n

my ($file, $rec) = split /\|/, $_, 2;

# Good idea, jdporter and BrowserUk
unless(exists $fh{$file}) {
  open $fh{$file}, ">> $file" or die "Can't open $file for append: $!\
+n";
}

$fh{$file}->print $rec;
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Or, as a one-liner:

perl -ne '($f,$r) = split /\|/, $_, 2; exists $fh{$f} or open $fh, ">> $f" or die "Can't open $f for append: $!\n"; print $fh{$f} $r;'

Update: I liked jdporter and BrowserUk's idea about caching the filehandles, so I added it. :)

bbfu
Black flowers blossom
Fearless on my breath