Since it is not currently possible to select Employee from the Assigned To dropdown on Task created from Partner Center, an alternate solution is to create a Custom CRM Field that sources Employee List and expose the custom field on the Partner Center Task Form:
A. Customize the Partner Center/APC role to add Permissions to View (Access Level) Employee List.
B. Mark Allow Viewing checkbox beside Partner Restrictions.
*As per field Level Help
Check the Allow Viewing box to allow users logged in with this role to see, but not edit, data for employees to which the role does not have access.
Note: This setting does not allow viewing of employee payroll or commissions data.
I. Create custom field "Assigned To Employee" to pull in the list of employees on the form
1. Navigate to Customization > Lists, Records, & Fields > CRM Fields
2. Enter value for Label (e.g. Assigned To Employee for Partner Task Form)
3. Select Type = List/Record; List/Record = Employee
4. Under Applies To tab, select Task
5. Under Display tab, select Main on the Subtab field
6. Click Save
II. Customize the Partner Task Form to make sure that the custom field created in Step I is exposed and hide the default Assigned To field
1. Navigate to Customization > Forms > Entry Forms
2. Locate the Task Form and click Edit
3. Under Fields tab, unmark Show checkbox for Assigned field
4. Make sure that custom field created in Step I is marked for the Show check box
5. Click Save
III. To send a notification email to the Employee assigned to Tasks created via the Partner Center, create a Task Saved Search and setup the Email Alert:
1. Navigate to Lists > search > Saved Searches > New
2. Select Task as Search Type
3. Under Criteria tab > Standard sub tab > add the following Filters:
4. Under Results tab > Columns sub tab > Add the following Task fields:
*This is the custom field created in Step I
5. Under Email tab, mark checkbox Send Email Alerts When Records are Created/Updated
6. Under Email tab, Recipients From Results, add the field:
7. Under Customize Message tab, customized the message of the email alert according to your preference
8. Click Save
*Employee assigned to the Task should receive a notification email when Task is created by Partner from the Partner Center OR APC.