LEO-to-GEO intersatellite links using laser communications bring important benefits to greatly enhance applications such as downloading big amounts of data from LEO satellites by using the GEO satellite as a relay. By using this strategy, the total availability of the LEO satellite increases from less than 1% if the data is downloaded directly to the ground up to about 60% if the data is relayed through GEO. The main drawback of using a GEO relay is that link budget is much more difficult to close due to the much larger distance. However, this can be partially compensated by transmitting at a lower data rate, and still benefiting from the much-higher link availability when compared to LEO-to-ground downlinks, which additionally are more limited by the clouds than the relay option. After carrying out a feasibility study, NICT and the University of Tokyo started preparing a mission to demonstrate the technologies needed to perform these challenging lasercom links. Furthermore, to demonstrate the feasibility of this technique, an extremely-small satellite, i.e. a 6U CubeSat, will be used to achieve data rates as high as 10 Gbit/s between LEO and GEO. Some of the biggest challenges of this mission are the extremely low size, weight and power available in the CubeSat, the accurate pointing precision required for the lasercom link, and the difficulties of closing the link at such a high speed as 10 Gbit/s.