Your employer has to sponsor you for one of the employment based categories, most likely Perm is the next step. There are other options that need to be considered, you need a consultation with an immigration attorney, can't discuss them on avvo, takes time and much more Information. You need to get started ASAP.
There is no such thing as a conversion from L-1B to a greencard.
L-1A yes, B... no.
Talk to the company's immigration lawyer .. not a non-lawyer in HR.
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maybe in a different country, as we do not have such a process in US immigration law.
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