Everyone knows all you need to log dives is a pen and some paper (this may or may not include actual dives, just kidding). There is really no way to verify them. The main purpose for a logbook is for your own benefit. If someone wants to check out your logbook how will they know the dives are legit. Without some formal verfication process we can only trust that that you are honest.
If you need the logbook for proof of experience, just record what you can from memory as mentioned above. Remember to change your writing style and pen color to look like you recorded them on different days. This way the "scuba police" won't try to pull your c-card.