With a capacity of 2200 mAh, I'm betting those are 18650
batteries that you found. If that is the case, then those will fit in the Prodigy V1, but will be too big for the protege. Also make sure they aren't primary cells, as those are not rechargeable.
For the protege you need 14500 batteries, those will be around 900 mAh. Both sizes are sometimes labeled 3.6V or 3.7V. They generally will operate between 4.2V and 2.75V, the variance is why when you are using a regular ecig battery, you will notice a decrease in the vapor production right before the battery shows as discharged(when it blinks at you that it needs to be recharged.)