Insert data in MSSQL from MySQL? (no replies)

So I'm currently inserting data into a MySQL table from a form on my Linux-based website. When a customer submits an inquiry through our web form, a new row is added to the specified table in MySQL. This works great.

On the other hand, our company has front-end MS Access application linked to data in our MSSQL database, and the hurdle I'm facing is getting the MySQL data (populated via the web form submissions) into the MSSQL database. We are not able to support the mssql or sqlsrv commands from web/PHP side of things due to a Linux-based web server. I've researched a lot and haven't found a way to connect the web server with the SQL Server.

I initially visualized a trigger since we want this action to take place on the MSSQL database as soon as a new row is inserted into the MySQL database, and only then. I was able to create a Linked Server in SQL Server Management Studio and query the MySQL data but I'm trying to issue an INSERT command from MySQL to MSSQL. I've seen documentation referencing the use of a trigger to perform the update but only from MSSQL to MySQL -- not the other way around.

Any thoughts on this? Thanks in advance!