What you are describing are tapeworms segments. Tapeworms are an intestinal parasite that pets can get either from eating fleas or eating mice. In the case of a dog, it is far more likely to be from fleas. Since you mention that he was flea-infested when he was at the shelter, I'm sure that is how he got the tapeworms.
Here is more information on tapeworms:
Please note: tapeworms are transmissible to humans! However, the WAY they are infected is by eating the flea, which is the same way the dog became infected. So, given that you have treated your dog for fleas, and neither your son nor your girlfriend is likely to eat a flea, the risk is very very low. Tapeworms can be treated with either Drontal Plus or Cestex. In Canada these are only available through a veterinarian.
Unfortunately, Nemex contains only pyrantel pamoate which is NOT effective against tapeworms.
Your pup may well have roundworms, too, which are much harder to detect and usually require a fecal sample to be examined by a vet. These are ALSO transmissible to humans, with children again being most at risk. Fortunately, the Nemex will have killed any of these. I would be far more concerned about the risk to your son and girlfriend from this worm, but since your pup has had 2 doses of an effective dewormer for this, that will get rid of them. Just make sure you pick up any feces from the yard immediately when the dog deposits them.
Here is an excellent website about pets and parasites and the risks to humans:
So, in summary, you are describing tapeworms. Because the Nemex is not effective against tapeworms, I suggest you take the pup to a veterinarian, or phone your vet to explain you have seen tapeworm segments. He will be able to provide an effective and safe dewormer. Here are links to products that WILL kill tapeworms.
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