Someone swiped my cake card and checked the surveillance. Can I send it to the group?

No. Posting it to a public platform is an invasion of privacy. Videos cannot be posted privately to public platforms without the permission of the person in the video, but whether it is illegal to post surveillance videos in a group depends on the content of the video. If someone inquires about personal information privately and there is evidence to prove that they have obtained it privately, it can be proven that it is illegal.