Answer:
No, they do not have the authority.
Step-by-step explanation:
As per the fourth amendment of US constitution police can do reasonable searches, and a search is considered to be reasonable only when they have obtained an arrest warrant to do so. It is generally known as probable cause. The police can enter allocation and search for a particular item after obtaining the warrant. The search can be expanded if evidence of crime is in plain view. Police can also perform a search if the home owner of the business gives their consent to do so. They can also search without a warrant if they are pursuing a criminal and the criminal enters a house to hide and also in case of urgent emergency when there is no time to obtain one.
The warrant is not valid in this case because they neither have the authority nor the consent to search the other address.