Sure, they can reject.
But, if you honestly told the US Consul about the convictions, and have all the court papers, and they weren't crimes of moral turpitude, you should be OK.
Consider consulting with an attorney.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship.Ask a similar question
If your convictions were known to the consulate and you were granted B-1 visas, then these same convictions should not be a reason for an L-1 visa to be rejected.Ask a similar question
Since the crimes involved moral turpitude, you might eventually be approved, but the convictions could very well result in a denial. Depending on the crimes, you will likely need a waiver and may be ineligible down the road to receive the L1.
Even if you previously received the B-1 Visas, this does not mean future visa issuance is guaranteed with prior convictions for crimes involving moral turpitude in your background. Also please note that three months time is a long time for administrative processing, but administratve processing in very unusual circumstances may go on for many months (even over a year). I write this, because it is possible the administrative processing may go on for months longer, only to result in a negative decision after its completiion
You will certainly be rejected, however you can apply for a nonimmigrant visa waiver.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.Ask a similar question