When in Recovery Mode, select Utilities on the Menu bar at the top of the display.

Click Terminal in the drop down that appears.

If you know, or have already found the exact file path for the folders you want, use the rsync or cp commands to copy the contents from your Mac's storage, to the connected destination.

The necessary command will look something like rsync -r /Volumes/"Name of your Boot Disk"/Users/useraccountname /Volumes/"Name of your External Drive"

Make sure to keep the quotations around the names of any folders with spaces in the names. A space is also required between the source folder and the destination to differentiate between the two.