To enable this functionality, a System Administrator would first need to enable the "Cases + Homes: Allow file attachments to be copied between a case/home's activities and reports" setting in the Organization Settings > Organization Preferences menu under the Settings tab.
(*If you don't see this setting, contact support to have this feature enabled in your system)
Copying File Attachments
To use this feature, open the activity or report you need to copy attachments to, and make sure the item is opened in Edit mode. Scroll down to the Related Document(s) section. Next to the Attach File paperclip icon, you should now see a second button labeled Add File From Another Activity or Report.
Click that button, and a new window will open displaying a list of all available activities and reports for the case or home that have files attached. You can search types or description by typing in the "Filter files" field.
To copy file attachments from any of the items in that list, click on the name of the item. The attached files will then automatically be copied into the Related Document(s) section of the item you are currently editing.
Once the file attachments are copied over, click Save in the top menu bar, and the copied files will be saved to that item.