Car tax question

Hi,

I have recently bought a Dihatsu and I have just MOTed, insured and taxed it (today). I still have my old car (a Ford) which is taxed until the end of September, as my sister says she wants it. I was wondering if it will be legal to keep the car parked at the side of the road for a few weeks until my sister comes to fetch it - since it is taxed until the end of Sept. Or will the remaining few taxed months now be void since I have moved my insurance to the Dihatsu?

Thanks in advance