Try reading the b file first and then match the words to those in a

#!/usr/bin/perl
use strict;
use Data::Dumper;

my %file2 = ();
open FILE2,'<',"./b.txt" or die "Cannot open b.txt";
while (<FILE2>){
  my @words = split /\s+/,$_;
  my $zz = join 'zz',@words;
  for (@words){
    $file2{$_} = $zz;
  }
}
close FILE2;
print Dumper \%file2;

open FILE1,'<',"./a.txt" or die "Cannot open a.txt";
open FILE3,'>',"./r.txt" or die "Cannot create r.txt";
while (<FILE1>){
  chomp;
  my @words = split /[ \.]/,$_;
  my @added;
  for (@words){
    push @added,$file2{$_} if exists $file2{$_}; 
  };
  
  print FILE3 $_,(join ' ',@added),"\n";
}
close FILE1;
close FILE3;
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