At the moment, our website creates quotations at the contact level.
Once we receive the notification we set up the opportunity & move the quotation to the opportunity.
However, this "change parent" move causes the pricing of the quotation to reset itself.
This is very troublesome as the customer has already made payment and the quotation must remain an exact match to the order they placed.
If you want to remove the price recalculation on all "change parent" actions, you can vote/comment on this idea: https://ideas.prospect365.com/ideas/SPA-I-1960
The price re-calculation was being incorrectly triggered when moving a quote/order between two contacts/opportunites/problems under the same company. I think this is the use-case you've described here.
In v84 this has been resolved so we have marked this as shipped.
However, completely separately to this, we're also looking again at the UX for recalculating prices as there are a lot of different use cases where some customers do or dont want prices recalculated...
A better solution would be to have a "Recalculate" option presented to the user when the parent is being changed. Then the user can decide if the quote should be recalculated or not. (This is already the functionality when copying/basing-on existing quotations)