And that, friends, is why you should meet in person ASAP after meeting online.
I know many, many people who met online, and I have to say that as the amount of time without meeting in person increases, the likelihood of the rel
ationship working out decreases. People build castles in the air, and as the time goes on, that castle become more and more elaborate. The only problem is that the more elaborate the castle becomes, the less likely it is that reality could ever live up to it. And whilst one of you might be building the castle, the other may be building a beach house with someone else entirely

.
I too am highly sceptical of his 'sick mother'. And even if he does have a sick mother, as MrsJWine says, most people lean on their SOs in times of need. They don't not speak to them for 3 months.
Unfortunately, OP, your friend needs to take this as a lesson learned, and move on. If I were her, I would send an email, simply saying:
Dear John,
As I have not heard from you in 3 months, I have taken this as a clear indication that you do not wish to continue our rel
ationship. This email is to let you know that I too consider our rel
ationship to be at an end. Do not contact me again.
Jane
Then I would eat a huge tub of ice cream and move on. And never, ever let any future online re
lationships last for more than a couple of weeks before you meet in person. If the other party isn't willing or able, the chances of THAT rel
ationship working out are slim to none.