No Worries at all!
TOMTELL:
You have absolutely nothing to worry about and the very simple fact that you are at home writing to this forum and not languishing in an Immigration Detention Center subjected to the horrors of Removal Proceedings is all the proof you need.
Allow me to explain!
First of all, not any and all crimes subject an alien to removal; an alien who is not a U.S. Citizen is subject to being apprehended, detained, and placed in Removal Proceedings if his indiscretions amount to what Immigration Court has termed "Aggravated Felony (A.F) for Immigration Purposes." This means that if an alien racks up two or more misdemeanor DRUG convictions at state level, he is now an Aggravated Felon for immigration purposes and subject to removal from the United States.
There are basically two types of crimes that will get an alien booted out, and they are crimes involving Drugs and those of Moral Turpitude. Anything else and I.C.E. is not interested and will not come looking for you. Therefore, convictions such as (your) simple solicitation, D.U.I., non-violent domestic disturbance, spitting on the sidewalk, and jaywalking (just to name a few) although noticed by I.C.E., will not become obstacles in the alien's immigration process.
If there was to be any problem with your conviction, you can rest assured that you would have been arrested a long time ago and probably back in your home country by now, and the fact that you have not been and are writing this question on this forum is the foremost indication that you have not been labeled a "Criminal Alien" by I.C.E. and company.
So, do not worry at all; go ahead and apply for the renewal of your Green Card which is mentioning the obvious here as your really have no alternatives, unless you are contemplating living here out of status which is a sure way of getting removed, a euphemism for deported which is what it used to be called. But just remember to answer the question about arrests and whatnot truthfully.
I don't know on what basis you originally obtained the Green Card, but if you have become eligible in any shape or form for U.S. Citizenship, then I ABSOLUTELY recommend that you apply to become a U.S. Citizen instead of merely renewing the Green Card.
It will all go well for you. Just don't get any more misdemeanors of any kind any more!
fredrikklaw