Step 1: Install and Export Themes.

Step 2: Activate Export Themes on the new site.

The plugin might give an error like above.  Ignore for now.

Step 3: Go to Appearance > Themes.  Check which theme is currently active.  Note the name of it.

Step 4: Go to Appearance  > Export.  Find the name of the theme and select it.  Click export button.

It will download a file.