@Massimo, one thing that would be great to understand better (and solve), cause it's sort of annoying from a customer/user perspective. I know this has been a topic in this thread earlier, and it might not be something you will prioritize as there are uncertainties regarding alliance. However, this will probably also be relevant if a similar award redemption will be possible in SkyTeam.
In your Star Alliance Award search it seems like you have set a limit on the length of connection to 8(?) hours. Below is two individual flights from SVG-CPH and CPH-ARN that are fully legal to book. However, due to the 8 hour limit on connections, this is not an option when searching online for a trip from SVG-ARN
Not sure if this is a quick fix or not, but to be honest, I think that increasing the limit to 24 hours (which is the actual limit when booking over phone) will cut a lot of the phone calls to your colleagues at the Star Alliance Award booking hotline. Many of the bookings I've made myself would not have needed assistance from your team if connections up to 24 hours were visible online. Other Star Alliance search engines like United Airline show connections up to 24 hours.
By allowing this, it will also potentially increase the number of available flights as there can be married segments or segments with O&D restrictions involving connections above 8 hours that will never appear on the SAS search engine, and these will also not appear when searching leg by leg.
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