Fill a solid corner topologically correct When constructing technical objects I often come to a point where I want to add something into a corner. I haven't found an easy way to do so in a topologically correct way.

As a simple example this would be the situation with the corner to be filled


And this is the target to be achieved:


Given how easy it is to extrude such a block, I wonder if there is no easy way here as well.

Solutions I've tried so far:


extrude one of the two adjacent faces -> this gives a topologically incorrect model which causes problems later on
add a cube of the desired size, and make a boolean union -> (almost) impossible to avoid creating small steps and quite cumbersome
extrude one edge and fill the three faces manually afterwards. -> this is topologically correct, but still a bit cumbersome
isn't there an easier way???
If you have F2 addon enabled, here is a very magical trick.

Pressing F when F2 is enabled, several things will happen:


If 1 vertex is selected, it will create a face from the 2 edges connected with the vertex in the direction/position of the mouse cursor.
If 2 vertices or an edge is selected, it will try to created a quad face with the adjacent edges/vertices.  And the result doesn't need merging or 'remove double'.
If 3 or more edges are selected, it will simply create a face with selected edges.  Result can be an N-gon.