Private group needs to share final product with another private group

Are your groups A and C O365 Groups/Stream groups?

If they are, and you have contributor rights on both A and C then you should be able to just go to the permissions for the video and add Group A as viewers.

If you don't have contributor rights on Group A, who needs to approve, you can set the permissions so Group A can see it, but you can't make it show up in their group in Stream (because you don't have contributor rights on Group A). 

Edit video > Permissions > In the Shared with drop down switch it to "People" > Look up Group A. 

What this will do is grant permission to Group A, but it won't show up in their group pages in Stream since you don't have access to contribute to their group. Thus if you send anyone in Group A a link to the video they'll be able to see it.