My girlfriend's grandfather was jewish. He is her mom's father. Can she still make Aliyah and receive all the benefits from doing that? If so, what would be the process? does she need to go to a special rabbi for a certificate? (e.g. a reform Rabbi?)
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She is not Jewish at all. She is not eligible to become a citizen of Israel under the 'Law of Return'. She can apply to immigrate as a non-Jew.
If she wants to convert she needs to actually go and convert with a real (Orthodox) rabbi who is an expert in conversions. The correct definition of a Jew is the first recursive algorithm.
A Jew is someone who
A Reform or Conservative rabbi is not valid.
If she wants to convert so that it will be accepted by the Israeli rabbinate, ask them for the name of a rabbi in your area that would accept her. She can also apply to immigrate as a non-Jew and attempt to convert in Israel.
You mention that she is your girl friend. Note that while a marriage between a Jew and a non-Jew is invalid according to Jewish law, the secular Law of Return does have certain loopholes which many Russian non-Jews took advantage of.
I am not a lawyer, nor do I know Israeli immigration law. You would have to consult a lawyer to see what non-Jewish descendents of a Jew would be accepted by the secular law. However, your question implied that she wanted to make aliyah as a Jew. My answer dealt with that aspect.