The controller in your photo is rated at 48 Volts and has a low-Voltage protection circuit which turns it off at Voltages under 42 Volts so it is not compatible and will not work with a 36 Volt battery pack.
Before purchasing a controller and motor that are compatible with a 36 Volt Samsung lithium battery pack the maximum continuous discharge rating of the battery pack needs to be determined so a controller with a maximum current rating that does not exceed the battery pack's continuous discharge rating can be sourced for the project.
Regarding connectors, we sell connectors for practically all electric scooter, electric bike, and electric go-kart speed controller on our connectors page.
Please let us know if you have any question.
Battery packs are commonly rated at either 36 or 48 Volts instead of 42 Volts.
We carry 12 Volt batteries that can be made into a 48 Volt battery pack on our batteries page.