回复：但是她没有开始用新的h1b, 等于新的无效而已吧？

The petition part is still good (upper 2/3 of the I-797) but the bottom third (I94 part) is useless, so you still need to transfer H1 anyway to get a good I-94 to start working for the company. The good petition part by the small private company will exemp you from H1 quota. if without that private company I-797, you will need to use a number that is not available (your current H1 I797 by university was not using H1 cap)