G-IV Captain reported flap control malfunction during departure climb resulted in a return to departure airport and normal configuration landing.

Narrative

On departure out of ZZZ; at 400 feet and adequate speed I as Captain and Pilot Flying called for flaps to be selected up. Everything was normal and passing through a few thousand feet around 200 knots the auto-throttles disengaged prompting me to search for a cause. At that moment I saw the flap handle was selected up and the flap/stab gauge was indicating that the flaps were still at 10 degrees. Following what I saw; we got a message in our FMS stating 'Flap input invalid'. I then prompted the First Officer to request a level off which was 13;000 feet and we kept the speed within flaps 10 limitations. I called for the 'Flaps fail to move/ Flaps lock up' checklist per the Gulfstream QRH. We then requested a holding pattern at ZZZZZ and a lower altitude. We began to troubleshoot while holding at ZZZZZ at 5;000 feet and 200 knots. That checklist didn't change anything so we elected to try the 'Flaps Alternate' Checklist per the Gulfstream QRH. Again the flaps stayed at 10. We then found that the flaps would move down beyond 10 but not back up to zero. We held at ZZZZZ long enough to get the plane below its max certified landing weight. We ran the appropriate checklists. ZZZ Tower [advised] for us; we landed in a normal configuration as the flaps did move to full. We landed on the longest possible runway at ZZZ.