Here is a six year old post that tells you how to get 3 elements across the thickness. Six years later, the Mesh details panel has a new look. The Proximity Gap Factor is the number of elements across the thickness. This works for all kinds of complex thin walled geometry.
Your geometry is a simple tube, so you can insert a Mesh Method: Sweep and a Face Meshing control where you set the Internal Number of Divisions to 3.
 Pick the body and then select the same end face as the source face.
Shared Topology is not going to work with 3 elements through the thickness. The problem is there will not be a row of nodes at the center of the solid element meshed tube. You will be better off not using Shared Topology. Instead use Bonded Contact so that the edge of the surface can be bonded to the face of the solid tube. This will be superior to Shared Topology because the contact elements will support the the rotational DOF of the nodes on the shell elements that a row of nodes at the center of the solid face does not support.
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