Can I connect two rechargable LI batteries of different specs in parallel?
It is generally a bad idea to parallel Li batteries unless you are capable of measuring (and matching) their internal resistance. Experiments have shown that even a 20% imbalance in said resistance can (approximately) halve their lifetime, in terms of cycles.

For Li batteries of different types, chances are that the imbalance in internal resistance will be huge on the milliohmic scale that matters here; the batteries in the test I mentioned were all of the same type and had resistance between 0.015 and 0.021 ohms. Still a mismatched pair lasted only half the cycles what well-matched paid did.

So I think this mostly rules out using different types directly in parallel. The currents circulating between the batteries you mention could in fact get dangerously high. What happens when one battery discharges? The Li batteries don't have nice linear curve near the end of their charge, but it drops sharply, which basically means that the other battery will see nearly a dead short.



So you can't safely parallel them directly; you'll need an electronic circuit to switch between them. I don't know off the top of my head a controller designed to work with different cells in the way you want. Maybe something exist though; see https://en.wikipedia.org/wiki/Battery_balancing for the general idea. In general, these chips are designed for imbalances on the order of a few percent. What you ask for here is an imbalance of roughly 30% in mAh ratings.