OK. Boiler is a combi with built in timer etc.
Stat. is battery powered so doesn’t need a permanent live.
Connection C isn’t required. Only A and B.
A is the connection from the boiler which goes live when the central heating timer switches on.
B is the return from the stat. which goes live when the stat. calls for heat.
The 3 core is a legacy from a previous boiler that had a mains powered stat.
You need to look at the boiler installation diagram and identify which is the output from the timer and where the switched live goes to inside the boiler (which will fire the boiler and run the pump).
The wires may already be connected, or you (I) may need to work it out.
What is the boiler make and model and I’ll look up the manual online.
I may need you to take the boiler cover off and take pictures. 😯
Rich.