Yes, you can use frozen water from the freezer of one brand of fridge or freezer in the freezer of a different brand. Frozen water is essentially just ice, and it doesn't matter what brand of freezer it came from as long as it has been stored properly and is safe to consume.
However, it's important to note that different freezers may have varying temperatures and settings, which can affect the freezing and storage of food items. So, if you're transferring frozen water or any other food items between freezers of different brands, it's a good idea to monitor the temperature settings and ensure that the freezer maintains a consistent freezing temperature.