The text crawl effect is done by erasing the old text and writing it back into the canvas again only with a shifted "X" co-ordinate. You can do erasing in several different ways. One is by just resetting the rectangle that bounds the text to the canvas background color. Another is to rewrite the text in its original position, but using the canvas background color as the text color.
Then again, if the UI supports clipping (and I don't remember for the case of JME), you could simply set a clip rectangle to only repaint the area that holds the text and update the X co-ordinate in the paint method. Which is the preferred way to do things in systems that do painting in separate threads. For one thing, the clip/paint mechanism usually makes most effective use of the available graphics hardware and isn't impacted by other UI events.
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