split each string and look for dupes ..

$a = 'PF01389   6   218 1   255 430.09';
$b = 'PF00691   PF01389';

my %counts;
foreach ( split /\s+/, $a ) {
    $counts{$_} = 1;
}
foreach ( split /\s+/, $b ) {
    $counts{$_}++ if exists $counts{$_};
}
my @common = grep $counts{$_} > 1, keys %counts;

if ( @common ) {
    print "correct\n";
}
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or, less verbose,

$a = 'PF01389   6   218 1   255 430.09';
$b = 'PF00691   PF01389';

my %in_a    = map  { $_ => 1          } split /\s+/, $a;
my @in_both = grep { exists $in_a{$_} } split /\s+/, $b;

if ( @in_both ) {
    print "correct\n";
}
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