fileA.txt contains what you listed as File A in the question. I put the content of File B into __DATA__.

#!/usr/local/bin/perl -w
use strict;

my(%products) = ();

open(my $fh, '<', './fileA.txt') || die "Could not read fileA.txt: $!\
+n";
while(<$fh>){
    chomp;
    my($key, $value)=split(/\|/);
    $products{$key} = $value;
}
close($fh);

my(@groups)=();
{
    local $/;
    my $string = <DATA>;
    @groups = split(/(?=Group)/, $string);
}

foreach (@groups){
    my $name;
    if(m/Group Name: (.+)/){
        $name = $1;
    }else{
        print STDERR "Could not find group name\n";
        next;
    }
    my(@prods);
    if(m/Product Name:\n(.*)\Z/ms){
        my $prod = $1;
        @prods = split(/\n/, $prod);
    }else{
        print "$name\n";
        print STDERR "Group $name didn't have any products\n";
        next;
    }
    print "Group ".$name."\n";
    my $total = 0;
    foreach (@prods){
        print "$_ $products{$_}\n";
        $total += $products{$_};
    }
    print "Total ".join('+', @prods)." = $total\n";
}

__DATA__
Group Name: Small
Junk: lll
Product Name:
AAA
BBB
Group Name: Big
Junk: ggg
Product Name:
AAA
CCC
DDD


#output
Group Small
AAA 10
BBB 20
Total AAA+BBB = 30
Group Big
AAA 10
CCC 30
DDD 40
Total AAA+CCC+DDD = 80
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