Hi Lankiy,
Here is a similar thread for your reference:
https://social.technet.microsoft.com/Forums/exchange/en-US/6d955724-de79-46a3-96ef-c00d1335f020/microsoft-filtering-manageent-servcie-stopped-thereby-kill-transport?forum=exchangesvrsecuremessaging
1. Since transport service is dependent on Exchange filter management service, I recommend you removed FMS dependencies from Transport via registry to check if you can start transport service. (Some unexpected problems might occur if
you modify the registry incorrectly. Therefore, I recommend you back up the registry before you modify it.)
On mailbox server, open regedit, find HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\MSExchangeTransport, and then remove FMS dependencies
2. Copy configurationserver.xml file from working server to affected server to start FMS service.
3. After copying cofigurationserver.xml we were able to start FMS service.
4. Added FMS dependencies to transport again.
5. Transport and FMS service started.
Best regards,