The best and most robust way currently is:
- Export the design to a cloud storage service like GoogleDrive or Dropbox
- Download it to your desktop/laptop computer
- Put it on a thumb drive from your computer.
- Load the design from the thumbdrive.
This clearly does involve several steps that one could imagine should not be needed. You could also,
- Save the design to the SD card.
- Load ES File Explorer (or any other network transfer app)
- Transfer the file via to your Local Area Network to the desktop/laptop.
- Put it on a thumb drive from your computer.
- Load the design from the thumbdrive.
With the right hardware and sufficient knowhow:
- Save the design to the SD card.
- Connect a USB-Go cable between your Android device and the embroidery machine.
- Load the design from the Android Device.
There are now devices that have are both micro-USB and USB thumb-drives. This potentially makes for a two step process.
1. Save the design on the micro-USB thumbdrive.
2. Load the design from the USB thumbdrive.
There are also custom hardware devices which could help like:
SanDisk Connect(TM) Wireless Stick Flash Drive
Which can with an app on your phone transfer a file to the thumbdrive with limited battery life wirelessly. Then simply plug in the device which will also act as a thumbdrive to your embroidery machine.
The easiest would be if your embroidery machine had network access and had custom app that allowed you to simply send the file to the machine. But, to the best of my knowledge such things do not yet exist (May 2017).