What is the ruling on dealing with entities that request price quotes, invoices, and claims for a specific amount, then pay the value without taking the mentioned goods, and replace them with other goods for their internal needs?

The basic principle is that this is not permissible because it is a lie and a defiance of those in authority. However, if the official in charge is negligent or unconcerned with the welfare of the facility, and lacks a valid perspective, and the only interpretation of their actions is negligence or obstinacy, then there is no harm in doing so, provided that they have been advised and made aware of their error, and they have not responded.