How to Transfer Files on to a Phone When PC No Longer Recognizes it?
Firstly, this shouldn't happen. Android's MTP is designed in such a way that it will handle any and every kind of internal memory structure your device has. Maybe your drivers are having an issue, it should show internal memory in your PC regardless of being portable mode or not.

Nonetheless, you can use apps like Airdroid or ShareIt to transfer files over your local wireless network. Just connect both devices on same WiFi and follow the instructions in the app. Airdroid is easier to use with less hassle and doesn't require you to install anything on your PC.

https://play.google.com/store/apps/details?id=com.sand.airdroid