Code-compliant undercabinet light wiring
You'll need a different box

The fixtures you're looking at use a different converter box than what you have linked.  In particular, you'll need a Jasco 44130 box in order to transition from the connectors on the lights you've linked to permanent wiring. For your application, you'll need one of those boxes at each end of the connection, with a Chapter 3 wiring method between them, such as 14/2 NM cable if the wiring is concealed appropriately, or a surface raceway (Wiremold) with 14AWG stranded THHNs in it if you want to run exposed wiring box to box.