When using the Create / Clone Issue(s) Post-function, there is no option to copy the remote links to the newly created issues. This article explains how you can copy over remote links (Web Links) from the source issue to the target issue(s) using a Groovy script.
Navigate to the workflow you wish to change and enter edit mode.
Select the transition you wish to edit.
Click the Post functions tab.
Select Create / Clone Issue(s) Post-function from the list of post-functions.
Click Edit to edit the post-function on the transition.
Select the Run a Groovy script after the issue is createdcheckbox under Post-creation script