How can I move existing tab to Firefox container?

Tabs can be assigned to containers via:

Mouse

Switch Container adds a toolbar icon which gives a list of the containers from which to select.

Keyboard

Search and Switch Containers allows you to switch the current tab's container by going to to the location bar and typing:

co <container name>

The container can not be changed for existing tabs, it can only be assigned when creating new tabs. There is an enhancement request filed for that, bug 1323873, maybe you could leave a comment there describing your precise use-case to show interest in that feature.