Like any wireless headphones, the Woojer Strap Edge is a Bluetooth receiver, not a transmitter. Therefore, to enjoy a totally wireless experience with your Woojer Strap Edge you need to connect both the Woojer Strap Edge and your Bluetooth headphones to the same audio source.
While iOS devices have a built-in Audio Share feature, it is only available to first-party Apple products, and therefore cannot be utilized with the Woojer Strap Edge. If you'd like to connect both your wireless headphones (AirPods for instance) and the Woojer Strap Edge to your iPhone at the same time, you will need an external Dual-Link Bluetooth transmitter (AKA Bluetooth splitter). This transmitter is able to stream to two devices simultaneously, and you'll be able to pair it with both your Woojer Strap Edge and Bluetooth headphones. With this method, you make no use of the mobile's integral Bluetooth and should turn it off before using the transmitter.
Remember you can always enjoy a wireless connection between your iOS device and the Woojer Strap Edge while the only wire involved is the headphones wire. Your Woojer Strap Edge will still be connected to your mobile via Bluetooth. This partial wireless configuration will also let you enjoy the Woojer Strap Edge's integral audio amplifier, which can improve the audio quality of your headphones. See more details here.
For more information about connecting Samsung devices and Bluetooth headphones using "Music Share", please refer to this article.
For more information about connecting other non-Samsung devices and Bluetooth headphones, please refer to this article.