I know you trust him, but because you were not there you cannot be certain what happened to cause his arrest and/or conviction. You're getting his side of the story exclusively. There should probably be a nagging feeling in you that matches the questions your family or friends have about this relationship.
Therefore, take a moment to genuinely reflect on how well you really know your boyfriend, as yours is a long-distance relationship and you're not around one another frequently. Even people who have been married to one another have been fooled by a partner. It happens, so consider it. A background check on him might divulge that there is information about him that you didn't previously know (e.g., prior convictions, addresses, bankruptcies, aliases, marital status). Or, it could confirm that there are no discrepancies in certain information you already have about him.
Even if you believe him 100%, assess whether he bears ANY responsibility for his predicament and whether he is owning up to it. Unless it's a case of mistaken identity, there are always behaviors he could have done differently. If you still want to support him, offer him moral encouragement in the form of cards and letters but not financial support.