1800mAh battery charge with 450mAh
In theory, yes, you probably can do it (sort of).  However...


You will lose a lot in the conversion, especially if your voltage regulator is linear rather than switching.
Even with 100% conversion efficiency, you can only charge the 1800 mAh battery to a fraction of its capacity - assuming it's a 5 V cell (probably unlikely) the 450 mAh would only be able to charge it to just under half-full.
I'm assuming that you're talking Li-Ion or Li-Pol batteries here.  If that's the case, then be warned that they're very sensitive to bad charging (overcharging in particular), and are liable to overheat and burst into flames if not handled correctly.  With the greatest of respect, from the tone of your question, I suspect that you don't really have sufficient knowledge and experience to do it properly.