Hello Jan, yes the Stealth will fit and will work incredibly well with your Kenmore System....we guarantee it. Hope you have seen the customer testimonials! The Stealth Kit for your wall inlets where the suction starts when the lid is opened is the kit for 1.25 inch inlets on this page https://builtinvacuum.com/help/kenmore.html. All you need to decide is if you want a 30 or 35 foot hose in the kit, and if you want to spend the extra money for Stealth II which has the easy to use hose connection and foot release from the Stealth itself (great for quickly disconnecting the Stealth and using the wands to clean closer to baseboards or spots the Stealth will not fit into (the Stealth is a generous 14 inches wide).