Hi @Alexander L
From your description, it looks like you are submitting emails from your application to the Exchange 2010 server and its not working. If my understanding is incorrect, please provide more details.
For that to work, please create a custom receive connector for application relay with the IP address of your application (php emailer) and then try submitting emails. Share the error message by removing personal information if its still not working.
https://learn.microsoft.com/en-us/exchange/mail-flow/connectors/allow-anonymous-relay?view=exchserver-2016#step-1-create-a-dedicated-receive-connector-for-anonymous-relay
https://practical365.com/exchange-server/how-to-configure-a-relay-connector-for-exchange-server-2010/
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.
Also, Kindly note that Exchange 2010 is out of support. Please upgrade to the Exchange 2016 to stay in supported version.
https://learn.microsoft.com/en-us/lifecycle/announcements/exchange-server-2010-support-extended#:~:text=Please%20go%20here%20to%20search,2010%20and%20SharePoint%20Server%202010.
https://assistants.microsoft.com/
If the above suggestion helps, please click on "Accept Answer" and upvote it