To move time records from one task to another, you'll need to have editing permissions.
You can move time records to another task via the Project details page or Time page.
How to move a time record in the Project details page -
In the Project details page, go to the Tasks section, and find the time record you'd like to edit.
Hover over the time record, and select the pencil button to edit.
The Edit Time Record modal should appear, then select 'Change User/Task'
Then in the drop down list, select the Project and/or Task you would like to move the time record to.
Click Update to save the changes.
How to move a time record in the Time page -
In the Time page > Drag and Drop, you can double click on the time record you'd like to move.
The Edit Time Record modal should appear, and click 'Change User/Task' to make those changes.
Select the Project/Task you'd like to move the time record to, then select Update to save the changes.