Last Updated: Sep 29,2013
(I have not posted this in the accessory section because I believe it is a problem with the phone
By default, as you've discovered, ringtones do not use the media channel and therefore will not ring through A2DP devices. At the very least, you'll hear your Bluetooth device's chime for an incoming call, but nothing more. The easiest way to get ringtones through speakers is to stick with old school 3.5mm speakers instead of BT. Unfortunately, I do not know any apps or tricks that can modify the phone into ringing over A2DP, or if there is a BT protocol that can pick up ringtones with a device to support it.
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