Stitching UVs gone wrong

I’m trying to stitch UV of a single face into the other face of a cube, so I select one edge of the lonely UV face and use UV > Stitch.
The problem is that, instead of moving that single UV face on the right side, it moves the other UV island, with 5 remaining faces (on the left side). I want opposite result - the big UV island must stay intact, while only that lonely face is supposed to be moved.

In other words, green arrow show the transformation I want to obtain, while the red one shows the transformation that Blender serves me.

Have you tryed the opposite order of selction? the edge from the big mesh first then the lonely face you want to stich?

Actually, I don’t select faces but edges, and it’s only one selection step, because Blender automatically finds the matching edge, selects it and treats as one. I don’t know if I’m explaining it well, but here there’s nothing like “select one edge, then another”. It doesn’t work like this in this case.

yes,you descirbed that the big mesh is moving.If you select the opposite edge order,in theory the small object should move and the big mesh not.Not sure if i descibred it well.(first and last active selection)

you could also pin your big mesh should work too.

What I’m trying to say is that there are no two selections. There is no distinction between selected edge and active edge. It’s all treated as one edge, because it indeed is one edge in 3D. It just looks like two edges in UV Editor. Wait a minute, I’ll post my Blend, and you’ll see.
Maybe it depends on UV editor settings, but I really played with them for a couple of minutes, and there’s no change in behaviour.

Here is a video how to do it

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I was preparing the answer when pixelgrip posted the video. I will post anyway.

When you use UV stittch you can use the I key to switch the static island.

After using the popup appears

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DNorman, yes, that’s it! Thank you for this solution.

I knew the video. Of course, I did my research first, and watched all videos about stitching on YT, but none of them covered the I key usage.