Britney filmed Sam as he gifted her a Dobie pup Friday. He posted the video with the caption, "Surprised my fiancé with our newest member to the Family ❤️ Porsha."

As Brit trained her cellphone on man and dog, you hear him say ... "Her name is Porsha and she's meant to unconditionally love you and is going to be trained to protect you from any motherf***** that comes around you with bad intentions."

You'll recall, Brit's had canine issues recently ... she got into it with her housekeeper after the woman took Britney's other 2 dogs to the vet because she felt they were being neglected. The dogs ended up staying with the dog sitter for 2 weeks until they were returned.

It feels like things are lining up for a post-conservator life. As we reported, our sources say Britney and Sam are in the early stages of looking for a new house, though they won't pull the trigger until the conservatorship is terminated. That could happen as early as November 12, the date of the next court hearing.