Peel the jaguas to remove the outer skin. Cut each fruit in half and scoop out the pulp and seeds. Slice the pulp into strips or squares about 1 cm thick.
Place the jagua pieces in a pot and add enough water to cover them. Bring to a boil over medium heat and boil for 5 minutes. Remove from heat, drain, and discard that water.
Return the jagua to the pot and add 1 cup of water. Cook over medium heat until the pieces are tender, about 15 to 20 minutes. Taste and cook an additional 5 to 10 minutes if you prefer them softer.
If the water level gets too low while cooking, add additional water ½ cup at a time to keep the fruit from drying or sticking.
With the pot still on the heat and some liquid remaining, add 1 ½ cups sugar, 1 pinch salt, 3 cinnamon sticks, and 1 piece lime zest. Stir to combine.
Continue cooking over medium heat, stirring occasionally, until a thick syrup forms and the jagua pieces are coated, about 15 to 20 minutes. If you prefer a more liquid syrup, add a little water, ½ cup at a time, until you reach the desired consistency.
Remove the pot from the heat and let the dulce de jagua cool to room temperature.
Transfer to an airtight container and refrigerate for at least 4 hours. Serve chilled.