Hello giseburt,
Here's my answer. It is possible, but it will require a bit of customization. Firstly, you have to copy New Activity screen and click on edit. Once you are in edit mode, you can add a grid to the Recent History section based on the DocumentLibraryLink table. Once the grid is created you have to assign actions to relate it to the Activity. (Check activities,opportunity, cases grid for detail). Assign actions according to your need and it should produce the desired result. You can also check the EditCase screen for the Document Grid setting, that will be helpful in assigning actions.
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-Inder