The case is currently under investigation. Until your friend is convicted and she has accepted the verdict or there is no option for appeal left, then she is convicted. Until then she can fill the option "no" when asked whether she is convicted in a criminal case.
Also, when the lawyer says "close the case" he doesn't necessarily mean conviction. This can mean any of the following:
- A conviction either a ruling by a criminal court or by a Strafbefehl, which is a written convition which your friend can accept to avoid any further proceedings by a criminal court. In this case she is convicted of a crime, although she might not be obliged to admit that (see below).
- Termination of the proceedings according to § 170 II StPO (German Criminal Procedures Code), which means not enough evidence could be produced to support further proceedings of a criminal court. This also includes the case of being proven innocent. In this case she is (of course) not convicted.
- Termination of the proceedings according to § 153 StPO. This happens when the prosecutors office finds that while she has broken a criminal law, her involvement constitues a petty crime that does not warrant further procedings in a criminal court. She is not convicted in this case.
- Termination of the proceedings according to § 153a StPO. That is similar to § 153 StPO, except that her level involvement is considered higher and she has to accept to pay a fine to avoid further proceedings of a criminal court. She is not convicted in this case, even though she has to pay a fine.
If she is actually convicted (the first case) and the punishement is a prison sentence (probationary or not) of less than 90 days or a fine equivalent to less than 90 days of average income and she has no further convictions (above, below or equalling 90 days) in her record, this entry in the record is considered non-public. That means that, while the prosecutors offices and any criminal courts involved in future proceedings can see her entry, it is not included in her public record. That means the transcript of her record that she can request from the authorities (called Führungszeugnis) will read "no entries". If - for example - her (prospective) employer asks her if she is convicted of a crime, she can legally say "no".
As I said, until there is a verdict, she can always say no. The question gets interesting when she is convicted, but to a punishment less than 90 days. While she can legally claim to be without a criminal record in practically all relevant situations in Germany, I can not say what point of view the overseas authorities have on this issue. Unless they can request her non-public record from the German authorities (which I doubt), they will have a hard time proving her criminal record, since even the official transcript would be empty.