In my earlier reply, I mentioned that you will want to backup the true source. For best results, you really want to be running Duplicati on \\computer itself to back up those files from the devices physically attached to \\computer and not your current workstation.
So what if \\computer is a NAS device with no OS to run apps or maybe you do not control \\computer so you can’t install software there? In those cases, you will want to backup the path \\computer\share\ not the drive letter. Duplicati is unable to browse network paths in the GUI as far as I can tell, for both Source and Destination selection. Just push the 3 dots and select Show advanced editor then put \\computer\share\ in the Source folders box. To provide network credentials, you will need to create a batch file with this command:
net use \\computer\share /user:barney password1
Then you can use the Duplicati backup option “run-script-before” under the Options tab to run this batch file before it starts any operation related to that job. If you are concerned about storing your network credentials in a plain text batch file, you can use a powershell script instead, which can use encrypted strings to store the password but its a little more technical. I just tested this with 2.0.3.3_beta_2018-04-02 on Windows 10 Pro running as a service with a backup account that has interactive logons disabled.