Because everything is in house they do all of that stuff electronically. They most likely would do it the same way even if it were not a PetSmart but to another veterinary office the same way, unless they kept records the old-fashioned way, then they would most likely make you copies.
You can ask the vet or groomer for your pets paper records. If the records are all electronic then the new vet or groomer should have access to them already.
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