When you put an SD in the phone, when you start to the camera app, it should prompt you about storing to SD Card. If not, find the settings and make sure storage is set for SD Card. However.....but....SD cards can get corrupted, or just stop working from one day, next day...not working. You need to make sure you have a backup plan to save precious memories. On the new phone's, Android has the traditional Gallery app to manage folders, but also had a Photos App, which will backup you photos into Google+/Google Drive. It gives you about 15GB of space. Careful. I am not sure it's Wi-Fi only, and may use your cellular data, which could eat data. Check it's settings. What carrier are you with? Dropbox is nice too, but only 2 gb of storage. Dropbox will auto update (defaults to Wi-Fi, but can use cellular data) up to its cloud.
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