I have found a workaround to my own post.

Instead of trying to assign a value to move_finished_ids field at the creation of a production/manufacturing order, I firstly created a production/manufacturing order without assigning move_finished_ids value and then updated the record later with the desired move_finished_ids value. See code snippet below:

#Step 1 - Create a M.O. 
newMO = {
        'product_id': 1579,
        'company_id': 1,
        'consumption': 'flexible',
        'date_planned_start': '2021-08-01 09:00:00',
        'location_dest_id': 8,
        'location_src_id': 8,
        'picking_type_id': 13,
        'product_qty': 1,
        'product_uom_id': 1
        }
models.execute_kw(db, uid, password, 'mrp.production', 'create', [newMO])

#Step 2 - Update move_finished_ids (in this case 330) in Manufacturing Order 71.
iD = 71
attr = {
        'move_finished_ids': [330]
       }

models.execute_kw(db, uid, password, 'mrp.production', 'write', [[iD], attr] 

This worked perfectly fine in my case. If you know how to combine two steps into one, please do let me know!