As part of your new method, you create a new HTTP::Request object. But in this new scenario, you already have an HTTP::Request object. So why not create a variation of your new method that works with an existing object.

sub new_from_http_request {
  my ($class) = shift ;
  my $self = $shift ;
  $self->{myA} = undef ;
  return bless $self, $class ;
}
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You can then do something like:

my $httpr = AnotherModule::f() ;
my $ownHttpr =
  My::HTTPRequest->new_from_http_request($httpr);
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Alternatively, you could use the same new method and just make it a bit cleverer:

sub new{
  my ($class) = shift ;
  my $self;

  if (@_) {
    my $self = shift ;
  } else { 
    my $self = $class->SUPER::new(@_) ;
  }
  $self->{'myA'} = undef ;
  return bless $self, $class ;
}
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In both cases, the code can probably be improved by using something like UNIVERSAL::isa to ensure that the parameter that you have been passed is actually an HTTP::Request object (or a subclass).