Question regarding agreed value poilicies

[Zippee]

If you have an agreed value insurance policy my understanding is your insurer will pay out that value straight away rather than have the usual hassle of negotiating from an unrealistically low initial offer.
However, what would happen if a 3rd party hit your car and was responsible for the write off? Would the 3rd parties insurer be immediately obliged to honour the agreed value you have with your insurer or would they try to offer book value only? The whole point of agreed value is to ensure a rare or hard to value car is free of the potential pitfalls of the above but does it work from both sides?

[GC8]

Your insurers pays you, and then claims from the other partys insurer.

[Zippee]

GC8 said:

Your insurers pays you, and then claims from the other partys insurer.

Great - thankyou.

[GC8]

If this wasnt the case then an agreed value policy wouldnt offer much in the way of benefit, I think.

[Zippee]

GC8 said:

If this wasnt the case then an agreed value policy wouldnt offer much in the way of benefit, I think.

Thats what I thought, I could certainly see it from my insurers side but was unsure if a 3rd party insurer would be bound by those terms as well.