Tia said she misses her dog “every day” and she was “like my little child.”
But she generously said she would give the dognappers all the money she has if it meant she got her back.
She turned 12 last Thursday (Aug 25).
In the video, Tia, of Uxbridge, west London, said in the message: “This is to the thieves, today is my birthday.
“And knowing that she is out there but not with me is really difficult.
“I really wanted to spend my birthday with my dog, having fun, doing really fun things, blowing out candles.
“But that’s not going to happen.”
She added: “And all I want to say is ‘If you stole her for money or for your pleasure, it’s not pleasure to other people.
“It’s not pleasure to me, it’s not pleasure to all of my family.”
Tia – who lives with mum Gintare Varlee, 37, and her husband Tomas Jagminas, 39, continued: “I really miss her every single day.
“She was like my little child.
“And if you are doing it for money, I will give you all of my pocket money, all of it just so I can have my baby back.
“She was my puppy, I wanted her forever.”