Producing Portrait orientation stop motion videos
This is most likely a problem related to the app you are using to create/view these stop-motion videos. If you have portrait-orientated pictures, creating a video accordingly is simply a matter of setting the right video dimensions (i.e. video width and height in pixels); basically every video editing software allows you to set this manually or choose from a number of presets. If your smartphone displays it like this:



the video was probably exported with incorrect settings, e.g. a widescreen preset; in that case, the video might contain black borders at both sides, which might be why your phone is displaying the video like this. How did you create this stop-motion video in the first place? Your questions sounds a bit like you used some smartphone app, which leads to all kinds of problems, including the video dimension and orientation issues you get when you can't set custom video parameters.

Edit: Since you used the windows-movie-maker tag, I should mention that this is the single most useless video editing program in all known and unknown universes, dimensions and planes of existance. The best solution to any problem related to Windows Movie Maker is switching to another program that actually does anything of what it's supposed to do.