If Maurice is in power, it's unlikely that the Byzantine-Persian War would break out, although if it (or something like it) did, Maurice was by all accounts a better Emperor on the whole than Phocas was, so it probably wouldn't be as devastating as IOTL.
We might see the Persians allying with the Islamic armies, although TBH I don't see this alliance lasting very long. Traditionally the Arabs had quite clearly been the junior partners in their alliances with Persia and Byzantium, and I doubt the Sassanid monarch would want that to change. The Muslims, on the other hand, believing themselves to be on a divinely-ordained mission to conquer and convert the world, wouldn't accept being second fiddle to a bunch of infidels. Even if the Byzantines get decisively defeated, therefore, we should probably expect to see an Islamic-Sassanid war break out very shortly afterwards.