You can assign tasks, calls and meetings to someone else from either an activity´s tile or detail. After you assign an activity, you can then share the recored with the newly assigned person.
Tile – tap the Assign button, then search for the contact and tap the Assign button.
Detail – on the Activity detail´s Participants section, tap the Add (+) and then add a contact to the Assigned to role.
How do I add or remove Participants?
How do I share records?