h1b transfer - Nonprofit to Profit

Hello,I got my h1b in 2013 from a consultancy subjected under cap. I have my I-140 approved now. Recently, I changed my employer and shifted to non-profit organisation. Does this mean my h1b becomes non-profit h1 and I cannot transfer to any other employer in future or since my first h1b was subjected to cap I can transfer to any other employer whenever I want.Thank you

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As you already went through the under-cap visa already in 2013, you should be able to transfer from non-profit to for-profit companies in the future. Check with your immigration lawyer to confirm.