copy custom text styles to new computer

I haven't tried this, but it might be worth a try:

Create a title that has all the styles that you want to transfer.

Export that title.  https://helpx.adobe.com/ie/premiere-elements/using/exporting-importing-titles.html

Copy the exported file to a flash drive from the old computer, and then copy it to a folder on the new computer.

Place the title in a new project.

Create a new style for each of the styles used in the title. 

Create a style

1. If necessary, double-click the title in the Expert view timeline to open it in the Monitor panel.
2. Select an object that has the properties you want to save as a style.
3. In the Style tab of the Adjust panel, right-click the object and choose Save Style.
4. Type a name for the style and click OK. A swatch displaying the new style appears in the Styles tab.

    

   from here:

   https://helpx.adobe.com/ie/premiere-elements/using/applying-styles-text-graphics.html

I've tried to figure out how to solve this since the question was posted.  I think that the custom styles are probably stored in files but couldn't figure out where.