What quest are you refering to? The one that pops up in your quest tab automatically every reset and involves you making donations to the syndicate chests and doing jobs? That one is account wide and has nothing to do with the weekly shipment rewards across from Spider. The shipments are tied to the syndicate vendors and can only be collected on the character(s) that finish their daily Priority Contract. In total you can get a max of 3 small and 6 large shipments per character per week. Or 6 medium and 3 large.