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I deliberately overlapped two UV-islands (on the screenshots) to texture them together and free some UV place, but when I unwrap the whole model (either via inner Blender algorithm or via uv packer addon) they unwrap separately and do not overlap.
How can I join/merge/group these two islands so they unwrap together?
Select the faces you want to be overlapped, set a view in which they overlap (front orthographic in your example) and press U > Project from view.
In the UV editor select all and press P to Pin this unwrap (or go to menu > UV > Pin).
Select all and Unwrap the model: pinned vertices will stay in place.
Alt P to Unpin.
