Copying a surface/solid body from a part to anothe

Hello everybody,

I'm in trouble with this operation; even reading the 2012's answer for this same question (https://forum.solidworks.com/message/709585#comment-709585). I supose I'm missing something basic, but I don't know what else to try... I explain:

While working into an assembly file (SW2016), I am editing a part that needs to be cutted by a surface offset of another part. So what I need is to copy the offset surface from the original part to the cutted (not yet) one. Now I'm describing the steps I do:

1. In the feature tree right click in the part where the offset surface is > Edit part.

2. In the surface body folder of that part I find my beloved surface and I right click on it > Insert into a new part.

On the prompt window I can only save the surface being a new part itself, if I choose the part where I want to add the surface directly through the prompt browser I have an error after the piece is opened as a new file in the SW session ("Error while saving the document"). If I don't choose a file with the browser and click OK I also have the surface opened as a no-named new part and I am only able to save it as a new part (obviously if I choose the surface-needing part I am asked to overwrite it, but never to add or combine both parts). So... I save my surface as a new part to try to add it to the other part.

3. Now I leave the "editing part mode" and click insert > part and into the prompt I choose the new part that contains only the surface. I'm not finding a merge, combine, add to part or similar option, so I can only add this part as a new one into the assembly as the tree shows after the part incorporation.

4. I still having the same problem: My cutting surface is into a different part to the one that needs to be cutted...

So my question is:

Between steps 2 and 3, how can I save the surface into the target part file instead of rewrite it?

or...

What am I missing?

PS: I think this can also be reached by exporting the surface to an IGES file or similar, but I'm trying to find the way to do it into a more simple workflow because there must be a way...

Thank you so so much!!