The best way my company has found to trasition data sets is to have another admin of the user group "take over" the data set. Following the steps below, an admin of the group can use their credentials to refresh a data set:
1) A group admin should login to Power BI Service and navigate to the noted group.
2) Select the data sets tab.
3) Click the "Schedule Refresh" button on the data set you want to take over.
4) In the Upper-middle of the screen there should be a button that says "Take Over", click it.
5) The person taking over the data set may have to enter their credentials after taking over to correctly refresh the data set.
You can repeat these steps for each other data set that the person managed. Unfortunately if the data set is in a place that only the person who left had access to (i.e. their desktop), the person taking over the data will not be able to refresh the data set.
Hope this helps,