If the Stylesheet is one that you have created on the first computer then it is local to that PC. The Stylesheet is not contained in the notebook unless you have created a private Stylesheet in that notebook using
Format/Edit Stylesheet... menu item to create the private stylesheet local to that notebook.
So, in your case, when you move your notebook to another computer it will not find your Stylesheet.
One way around this is to actually make a private Stylesheet in your notebook using the style definitions from the Stylesheet you have created. To do this open that Stylesheet, copy all of its style definitions, then paste those style definitions into the private stylesheet of your notebook using the
Format/Edit Stylesheet... menu item.