1. Install the addon called "uv-align-distribute".[github.com]
2. Open UV editor, then the n-menu. Addon is called "Tools." Make sure "Relative to:" is set to "UV space."
3. First select an island to be used as reference for scaling all islands, then rest of the islands that need fixing. Downscale them a bit and move them roughly to the middle.
4. Press "VCenter" button (the button with the line striking in the middle) to center all uv islands, then "Eg. scale" to match automatically all selected UV sizes.

Even if the face count is different with multiple islands, all UV islands share the same borders now.

You can also use the match islands to try to even the vertices' locations if your work requires that, though you probably want to keep the same shape of the UVs if you're reworking existing islands.