I don't quite follow the description.
Are you saying the machine had one type of switch, and when it failed you got a replacement which is the same ? Or is the replacement different ?
If it's the same then you just need to make a note of what goes where and connect the new switch just the same. If it's different then you've a bit more work.
You mention three flexes, one is the supply, one to the motor, what is the third ?
Normally, these starters come with diagrams for the various connections, and you should follow that. For single phase you normally put the neutral through one main pole, and the live through the other two - it goes through one, then loops back and goes through the other*. Most likely from your description, you'd connect the supply to L1 and L2, link T5 to L3, and connect the motor to T4 and T6. BUT you must read the instructions that came with the starter as it may need the live & neutral to be connected to specific terminals for the coil circuit to be powered.
* This is so that the load current goes through all three poles of the overload - otherwise it doesn't work properly.