This present paper is an integral part of another paper which completes the work (Int. J. Mod. Anthrop., 2018, 2:147-161). This part is about Moonrise observations and calculations which have been found from Cheeseboard/"Quesera" monument at Lanzarote Island in Zonzamas archaeological area in Canary Islands (Spain). This present paper shows that both a Sun calendar and a Moon calendar adjusted to fit into 29 or 30 solar days months are represented within this Lanzarote prehistoric monument. Age of built is not calculated by absolute methods, but other archaeological items throughout Lanzarote have been dated by C14, between 2nd/1st millennium BC. Genetic, cultural Atlantic and Mediterranean Megalithism and other archaeological / cultural traits suggest that this Cheeseboard/"Quesera" may be included in a Megalithic/Bronze Age context which may not be coincidental with this Age in other areas. However, megalithic findings in other Macaronesia Islands (Azores, Madeira, Selvagens) strongly suggest that Canary Islands may also have megalithic culture artifacts. It is possible that people massive emigration that occurred after Sahara desiccation may have also reached Canary Islands in addition to Western Europe and other areas and they may be related to these monument builders. Rock carved strips and ridges, "car-ruts" (megalithic in Malta) which occur in Azores, Lanzarote, Malta Islands, Turkey, Iberia and other World areas, supports a common and ancient culture origin. In any case, builders are more ancient than those who may have received Punic or Roman influence.