Hi Peter! I had a question about H1-B visas. I was approved for a H1-B in the April, 2014 lottery and received my I-797 approval notice. But I never activated

Hi Peter! I had a question about H1-B visas. I was approved for a H1-B in the April, 2014 lottery and received my I-797 approval notice. But I never activated it since I changed jobs to work for an international organization under the G-4 visa in September, 2014. I'm now looking to go back onto the H1-B visa with a new employer. Would I need to go back and ask my new employer to apply for my H1-B in the lottery again? Or would it be possible for my new employer to transfer my previously approved H1-B petition? Also, if it is possible to transfer the old visa, is there any time limit on its validity before I'd need to go back and apply via the lottery again? Thanks!