When holidaying in Fuerteventura a few years ago I went to Puerta de la Cruz but didn't see any obvious airstrip. We drove to the Atlantic side of the island through a little hamlet called Cofete and in the distance saw a large remote building which reputedly was used a a Nazi Operations centre during WW2. . Not sure if it is true but a Google search suggests this buildingit was used by the Nazi's so it's possible the airstrip may have been connected with this..