Dear Panama Jack and chitolin, many thanks for the information.
I failed to check the site for a while and already in Managua, I had a chance to visit INAC at the Managua Airport. They also provided me the same Golden Wings name and Captain Marlon.
He told me the same procedure saying firstly I need to convert to Nicaraguan licence.
What is not clear for me is that even just for flying with the pilot/instructor, is the conversion required?