I do not have the reputation to add this as comment to @Sourav Ghosh's answer, so adding as an answer itself.

New employee - N

Former Colleague - F

Manager - M

As mentioned in the question, since M knows about it and to avoid any awkwardness for F who is already suffering from the illness, I say, instead of telling N to talk to M, inform M, if it is a viable option, to talk to N or find any other way to have this situation addressed so that F does not have to go through this again.

That way, since this information is coming from the higher up, it has more value and s/he would know that the condition F is experiencing, has been acknowledged at the organization and not something you are making up to protect F.

Also, since you do not work there, you do not have to worry about thinking of this as going behind N's back. You're just trying to save the awkwardness for everyone and adding credibility about F's condition by having it addressed from the management.

I do not have the reputation to add this as comment to @Sourav Ghosh's answer, so adding as an answer.

New employee - N

Former Colleague - F

Manager - M

As mentioned in the question, since M knows about it and to avoid any awkwardness for F who is already suffering from the illness, I say, instead of telling N to talk to M, inform M, if it is a viable option, to talk to N or find any other way to have this situation addressed so that F does not have to go through this again.

That way, since this information is coming from the higher up, it has more value and s/he would know that the condition F is experiencing, has been acknowledged at the organization and not something you are making up to protect F.

Also, since you do not work there, you do not have to worry about thinking of this as going behind N's back. You're just trying to save the awkwardness for everyone and adding credibility about F's condition by having it addressed from the management.

I do not have the reputation to add this as comment to @Sourav Ghosh's answer. But as mentioned here, since the manager knows about it and to avoid any awkwardness for someone who is already suffering from the illness, I say, instead of suggesting the new employee to talk to the manager, inform the manager, if it is a viable option, to talk to that employee or find any other way to have this situation addressed so that your former colleague does not have to go through this again. That way, since this information is coming from the higher up, it has more value and s/he would know that the condition your former colleague is experiencing has been acknowledged at the organization and not something you are making up to protect your former colleague. And since you do not work there, you do not have to worry about thinking of this as going behind the new employee's back. You're just trying to save the awkwardness for everyone and adding credibility about your former colleagues condition by having it addressed from the management.

I do not have the reputation to add this as comment to @Sourav Ghosh's answer, so adding as an answer itself.

New employee - N

Former Colleague - F

Manager - M

As mentioned in the question, since M knows about it and to avoid any awkwardness for F who is already suffering from the illness, I say, instead of telling N to talk to M, inform M, if it is a viable option, to talk to N or find any other way to have this situation addressed so that F does not have to go through this again. 

That way, since this information is coming from the higher up, it has more value and s/he would know that the condition F is experiencing, has been acknowledged at the organization and not something you are making up to protect F.

Also, since you do not work there, you do not have to worry about thinking of this as going behind N's back. You're just trying to save the awkwardness for everyone and adding credibility about F's condition by having it addressed from the management.