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It seems not to work directly by selecting the faces, because the software can't guess where exactly you want to place the other part or even which of both should be moved to bring them together.
I found a way to merge your two parts with the given tools.
-Select the whole small part and use the Move-Tool.
-Anchor the grip to right surface of it and select just the green axis of the grip
-The "Align to Object" option sould be available, click it, then click on the upper face of your plate. The red (relating to your picture) surface of your small part should now be faced downwards.
-Rotate your view so you can see the downside of the small part, and anchor the grip now to the red surface. Again "Align to Object" to the upper surface of the plate.
Now your part should be angled so that the red surface is in one line with the other surface.
Now you have just to move the part on the same level of the big surface, place it where you want it and combine the two solids to one part.