Can I file a claim for water damages for items that were in storage from a claim that has been settled before? 
If I am reading your post correctly you had a water loss that damaged some of your items . The ones that were not destroyed were also not repaired and just restored in another unit . If this is the case the potential damage in question is from the first claim and not the second and I would suspect that your claim would be denied.If you can show youritems were fully repaired then the second loss is a second event and they may be coverage ifyour policy provides . Water damage from forced wind and storm is a covered peril unless excluded in your area but mold , if covered will have a specific sub limit . I would recommend you find a better storage facility that does not leak . 