Copying files from PC to "external" SD card
If you're not insisting on a wireless transfer, using an USB cable would give you at least two options:


Using mtp
Using adb


With MTP, on connecting the device to your computer you should usually get the option to open it in some file explorer (does so on Windows and on Linux at least). For ADB, you could use adb push to push files to your SD card – or, for your convenience, use an ADB GUI (some are listed here at my site.

For the latter, once connected via USB cable you could make it switch to TCP mode if you need it wireless. Without root, this must be repeated after each boot – with root, there are ways to initiate it without a cable.

Details can be found e.g. via the corresponding tag-wikis: adb and mtp.

Disclosure: The first two links lead to my Android website.