chestnut puree quantity
Assuming the chestnut puree is just chestnuts, well, use 250g of it.

If it has other ingredients... I guess you'll have to try to figure out how much of them. You might be able to deduce it from the nutrition facts and the nutritional content of the chestnuts themselves, especially it's just chestnuts and water.

Edit: To be clear, I'm telling you how to replace the chestnuts. You still need the rest.

Given that it's chestnuts and water, it's trivial to figure out how much of it is chestnuts.  (It would be difficult if there were other ingredients providing nutritional content.) Just use enough paste to account for 250g of chestnuts, then remove a mL of milk for every extra gram of paste you've added. If it's a substantial amount, replace some of the remaining milk with cream to keep it as rich as the original, if you like.

For example, according to the data I linked to, chestnuts are about 10% sugar, so you want enough paste to provide the 25g of sugar your 250g of chestnuts would've provided. So if the paste contains only 8g of sugar per 100g of paste, then you'll want about 300g of paste, and you can remove 50 mL of milk to balance the extra water you'll have added as part of the paste. (At that point it probably wouldn't be worth bothering to rebalance the milk and cream, since it's such a tiny difference.)