Well Woofgang is here but with nothing much useful to add this time I am afraid. Sqad has nailed it in his post. There is no short cut or quick way, all of us wish there was. Post stroke depression is very common and has three main causes. A person can be affected by one, two or all three and its often hard to tell what is happening. The first is bereavement, grieving for the person he was and will never be again and for the abilities he has lost. This is part of the reality hitting thing. Like any kind of bereavement grief, its a process that is individual to the person and will take as long as it takes to resolve. Close people can help by being there, calm, patient and not expecting too much.
The second cause seems to be purely neurological and a part of the stroke. Not everyone gets this but it is seen in some people....also of course its very hard to unpick what is causing anyone's depression and to what extent so this very hard to be sure about.
The third cause (and I mean this kindly but it has to be said) is caused by the behaviour of those close to the patient.....by their kindly meant expectations and "attempts to motivate" This can make the person who has had the stroke feel like a failure and a loser. Relatives and close friends mean well but there has to be patience in bucketloads and realism in how they behave. Love accept and appreciate the person who you have. Make it clear to them that they are not failures because their recovery is slow or does not come. Time and again I have seen and heard loving and well meaning relatives say that they have postponed things "until Dad is better" "until bro can walk again" and so on. Can you imagine the pressure this puts on someone who is struggling to make sense of new disabilities or the exacerbation of existing ones?
Of course with your brother, his pre existing problems might be a factor too. I am not aware of research on how someone on the autistic spectrum is affected by stroke but it would seem possible/likely that there will be changes not seen in someone who is not on the spectrum. Both Autistic Spectrum difficulties and stroke can have a marked effect on how people see and interpret the world and I would imagine a mix of both would add to the problems of recovery.
It sounds like he is getting good medical and rehab care and you are a loving sister. I would urge you to also be a patient one....support your brother of course but maybe back off a little on the attempts to motivate?