First of all, open the camera and, in Settings, set the default storage to the external sd card and take a picture. This will create a folder on the sd card and it makes sense to move the old pictures there. It will also make sure that future pictures are stored on the card rather than the phone.
Now, in ES File Manager, navigate to the folder where the photos are. It's probably called either DCIM or Pictures and there may be a sub-folder (on my HTC it's 100 Media). The file names are likely to begin either IMG or DSC followed by a sequential number.
If there are check boxes by the file names, you can select by tapping there, otherwise it's tap and hold to do so. Multi-select all the pictures you want to transfer. Now choose "Copy" and navigate to the equivalent folder in the sd card, where you'll see the test photo you took earlier. Select Paste. If the you get a notification that one of the file names exists, choose Overwrite as it's just the test image and you can lose that.
Now go to the Gallery app and make sure you can see the images on the sd card (you'll probably see two copies of everything). If it's all OK, go back to the original files on the internal storage, repeat the selection process and delete them.
You could also install Dropbox, sign up for an account and set it to sync photos (preferably over wifi only to conserve mobile data). This will upload them to cloud storage as a backup. You can also install Dropbox on a pc and the files will then store there as well.
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