Storing them in a paper bag for a few days will also help them along. When stored properly a mango should have a shelf life of about a week and while the mango will not ripen in the refrigerator, it can be kept chilled there once ripe, or it can be frozen, dried, cooked in syrup or puréed. To get the best taste out of your mangoes, follow these simple storage tips:If you find your mangoes are not quite ripe enough, store them at room temperature between 18 -22°C and out of the sun for a few days until the fruit ripens.