Copying lookup column value from one SharePoint list to another

Hello.

I am having some difficulty when I try to copy the values in a SharePoint lookup column from one list to another.  Both lists have the same lookup column called "Sponsor" and they are both referencing the same list called "Sponsor Values".  The Sponsor column is also a multi-selection drop-down in both lists, so I need to copy over all values.  The Sponsor Values list that is being referenced only has columns ID and Sponsor Name.

I have a Power Automate flow setup that copies information between list A and list B, but the Sponsor field does not copy over.  Can anyone help with how I need to go about doing this in Power Automate?