Are you doing this yourself or getting an electrician in? because the latter should be able to chain the two groups together by running wires behind the wall -- for that matter, you should be able to control the whole thing with a switch (either underneath or on the wall)...

Initially thinking to do it myself. That said, I have no experience in fishing wires or any electrical work..

Great DIY Project. Works out to about $5/ft. Links below are clickable.

Here's a video below - this guy used connectors - I thought soldering was easier and cheaper.

Installing undercabinet LED strips

I suggest watching other videos also, search youtube on "led under cabinet lighting installation" and you will find several. Here's a list of the things I ordered from Amazon:

power supply - $9
LED strip lights - $15 for 16 feet
26 gauge wire - $7.60 for a spool to connect the LED strips (solder)
Aluminum channel diffusers - $27 for 5 pieces of 1 yard each
Dimmers - $10 for 3. Optional parts

There's remotes that handle two LED strips with one controller, example link below (make sure remote matches the strips you buy). Jumping the two cabinets is the challenge - could do it across the top of the window and paint wires white (mostly hidden).

Dual LED strip controller

Better idea - no wires - WiFi LED strip controller - just need to find one that controls both strips simultaneously

LED Wifi Controller

Power supply?

The LEDs work off a 12V adapter that plugs in the wall linked above. Remotes have internal (usually coin-type) battery.