The length and accuracy of a dog's memory is debatable. Most experts agree that any semblance of long-term memory a dog has is associative rather than real. That is, a dog might remember her puppy based on something she came to associate with that puppy, but would not be able to recall her puppy without some associative prompt.
Dogs Remember Their Owners
Search the Internet, and you'll find countless videos and stories about dogs being reunited with their owners after months, or even years. Whether this memory is associative, prompted by their owners' voices or body language, or what experts call real, the dogs give every indication that they remember their owners. There is no reason to think this capacity for memory could not extend to their puppies.
The Memory but Not The Meaning
Mother dogs may remember their puppies if they encounter their puppies as adults, but dogs do not show any indication of forming familial bonds the way humans do. They are pack animals by nature, and establish their relationships based on dominance within the pack. So while a mother dog may remember her puppies, she likely will not care much, that they are her puppies.
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