When I connect my mophie product that is attached to an apple 5S phone, I tunes does not recognize the phone, so I can not synchronize the phone. My computer does not recognize the I-phone either. The original I-phone connector works though.

SKICAT9 wrote:

Why can't I sync the phone utilizing the Mophie USB connection to my computer?

Only mophie would know that. But according to their support page they are aware of the issue:

Mophie wrote:

Do I have to take my iPhone 4/4S mophie case off to sync with iTunes?

Negatory. Sync and charge all you want with the mophie micro-USB cable that comes with your case.Although our iPhone 5 juice packs do NOT support data syncing, wireless syncing is a solid alternative. Here’s a short article on how to set this up: Wireless Syncing with iTunes

Its up to Mophie to resolve this with their iPhone 5 juicepacks.

http://www.mophie.com/frequent-questions

You may want to contact Mophie about it so they know there's interest in them fixing this.

So far as I know, you can not sync your iPhone 5, 5s or 5c with your computer via USB when you have it in one of their juicepacks. You must sync it over WiFi or remove the juice pack. I seem to recall that being made fairly clear on the box the juice pack comes in.