The picture below was published in at least three different publications, so it seems to be the definitive proof that Havana did indeed get a fountain. Besides the mention of one publication (The Cuba Review published from 1907-1931) found under the picture, a 1912 publicaton called "Our Dumb Animals" published by three humane organizations had this same picture sent to them by a humane worker in Cuba detailing the delight of the people with their new fountain even claiming they would be happy to get another. The fountain had reportedly been offered to Havana through the Havana Band of Mercy by the National Humane Alliance. Jeanette Ryder had founded the Band of Mercy and gotten children involved in humane causes, and her work was documented in a publication called "The Gospel of Kindness" by Janet M. Davis. We want to thank Brittany Luna for tracking down that publication as well as locating the likely site of the fountain in the San Francisco Square in Havana. Her further research has turned up that the fountain was located in another park called La Parque de la Fraternidad Americana for a short time and eventually was moved to the intersection of Malecon & Avenida 28 until at least 1962, but no further information is available. She also tracked down the pictures below showing the setting in front of the Commerce Market Building.
For more on the National Humane Alliance Fountains click here.