Dear Theist prabhu,
Hare Krishna!
We don't say that brain has no involvement. But we ask the question that why does the brain does'nt function when a person dies?
What is the power which is making the brain work? We try to bring the point of discussion to the conciousness which is the property/characteristic of the soul!!!
As far as I've read from the scriptural books the little knowledge that I have tells that memory etc is the function of the mind and mind is not consciousness.
As Krishna said
Bhumir apo nala vayur, kham manah buddhir eva cha,
ahankaram itiyam me bhinna prkrtir ashtada.
"So Earth, water, fire, air and ether (which our body is made of) and then the mind, intelligence and false ego. They are the separated material energy of Krishna! Therefore the process of memory which is the function of mind/intelligence is material.
And then He says:
Apareyam itas tv anyam, viddhi prakrti me param,
Jiva bhuta mahaabaho, yayedam dharyate jagat.
So here Krishna says that there is a superior prakrti as well which is running this world and that is the soul. So Krishna has distinguished the two.
So I think that the more spiritual we become we have less material thoughts. That is, the mind is still there, but it is becoming purified As Narada Ji said " tat paratvena nirmalam " i.e., the mind and thoughts are getting purified. If the person who is advanced in spirtual thoughts can forget all material thoughts remaining in this world itself then how can he remember that in the spiritual world when he is serving Krishna personally?
Krishna has given me a good idea to prove the subtleness of human memory.Consider for example if we want to increase the memory of the computer which is a material object with no consciousness, we have to insert extra RAM blocks into it. If we thought that memory is the same for human beings then we also will have to put an extra block in our head to increase our memory, which is not the case. But contrary to this, We can increase our memory by increasing our concentration, which in turn comes from the consciouness!!!
Hence proved that memory is subtle
Apologies for the length of this posting and also if I've said something wrong here which is not in the shastras!
Let Krishna help us all in reaching Him!