Store files from any app to SD card via «Share to...» option.

How to do:

1. Start an application which offers to share files.
2. Select a file you want to store on SD-card.
3. Tap on the «Share» button.
4. Now you will face a «Complete action using» list. This is a list of installed applications on this device which offers support for the file type of the selected file. You will find «Share To SDCard» in this list. Just tap on «Share To SDCard».
5. Now you will face the file dialog for creating a new document. In the upper left corner you can choose the destination. Select a destination folder where you want to store this file and press the «Save» button in the right down corner.

To cancel the action just press the «Back» button.

More information here:
https://tech-c.net/posts/share-to-sd-card-for-android/

Note:
This application doesn't need any permission!