I downloaded the FREE DJ Lite, then purchased 'Play'

These were downloaded to my studio 'Tower' PC, as my laptop was off for repair.

I usually DJ out with Ableton, but a friend said to try Serato. Must be said I am loving it.

I've now got my laptop back and downloaded DJ Lite onto it. I then went to add 'Play' to it, but it seems the only way to do it, is to purchase it again ? Is this correct ?

I would have thought I could have downloaded it again from my account onto my laptop?

Does anyone know if this is possible, or do I need to buy it again for the laptop ?

Thanks

Matt