It is possible to clone checklists created with Issue Checklist for Jira Free or Issue Checklist for Jira Pro. Please make sure to enable the custom fields integration within the Issue Checklist for Jira “Global Settings”:

Please note that enabling the custom fields might take multiple hours until all issues have been updated. You can see if an issue has been updated by showing the “Checklist Text” field as a column in the advanced issue search.

Once all issues have been updated, the checklists should be cloned by Deep Clone as long as the “Clone other editable fields (not shown in "Create issue" screen)” option is enabled (it is enabled by default).

Checked items remain checked after cloning.