If only a manager allocated to a certain customer responds to their cases, set up an auto-assignment of that manager to all customer's cases.
Let's take a look at the steps required to implement such logic.
1) Add an additional field "Manager" to the user fields (administrator account — section "Channels" — subsection "Data fields"):
2) Import the customer list and their assigned managers to Deskie using a CSV file or via API.
3) Create rules for new cases, according to which the value in the "Manager" field will be checked, and then the necessary person will be assigned: