After the death of Professor Dumbledore in HBP, there has been much speculation on whether or not Dumbledore is really dead, and how he might affect Harry from beyond the grave. There have been several theories advanced, yet the best method Dumbledore could use has not been mentioned yet; Dumbledore’s Pensieve.
Surely Dumbledore, being the greatest wizard of the age, was sufficiently prepared to die that he had some plan figured out for the event of his death; a will, or something of that nature. However, Dumbledore knew that upon his death, if Voldemort were not already killed, there would be some need for the knowledge that he possessed, and how it would be passed on to Harry or some other custodian would be a huge concern. He recognized that Voldemort’s history and any other information he (Dumbledore) had obtained were not safe to be written down, for it would be too easy to open a book and read the information, which we already know Dumbledore wished to keep confidential.
Enter the Pensieve, which would be an excellent way to preserve Voldemort’s history and information without committing it to writing, which has a major confidentiality problem. Basically, a thought can be pulled out and put away in a small jar, and no one would know what it was unless they were specifically looking for a Pensieve and the thoughts that it would unlock. Apparently, a Pensieve is not a normal possession for a wizard to own, since it is not mentioned anywhere else in the series, and more than likely it is easily overlooked by the general wizarding populace, simply from ignorance. Memories are easily stored, as we saw, and if a wizard did not know what it was, he would be none the wiser on what he was looking at.
So yes, it would be easy to take the memories he had and store them in a secure place. A couple of protective hexes or other enchantments could keep it safe. Dumbledore is clever enough to come up with some doozies here! A letter enclosed with his will, addressed to Harry, telling him where the memories and Pensieve are, and how to retrieve them from the enchantments placed upon them, and Harry is in possession of a lot of valuable information that would be very helpful in his search for and fight with Voldemort.
What might these memories be? Well, Dumbledore’s memories of Snape are one mystery a memory could clear up; it is not made clear in book 6 exactly WHAT it was that Snape said or did that convinced Dumbledore he was truly sorry. While it’s obvious Dumbledore is trusting, he has demonstrated (in his interactions with the young Tom Riddle) that he not is THAT trusting. An apology would not be good enough. There would have to be something else.
Aside from the history of Voldemort that Harry has already seen, what else might Dumbledore know that would help Harry in his fight? There are a couple of possibilities here: first, there is the memory of the other horcruxes and how they were disabled. In watching this, Harry would gain valuable insight into how Voldemort thinks when he’s choosing and hiding his horcruxes. We are two horcruxes short in the final listing. We know they belong to Gryffindor and Ravenclaw, but we have no idea what they could be. Perhaps by studying memories of other hidden horcruxes, Harry will come across a clue that will help him divine where and what these are.
Secondly, there could be a greater record of Voldemort’s past activity. We only saw Voldemort’s history up to his application at Hogwarts, we saw nothing from his reign of terror. Surely Dumbledore knew more about that than Harry was given access to before their lessons were ended. This might also give Harry clues as to where and how to defeat Voldemort for the last time.
This is really the best, most logical way for Dumbledore to impact Harry in the next book. JK has never allowed her characters, once dead, to reappear in any way that might indicate they are still alive, but as a memory, it is plausible. She has already shown that this is possible in Chamber of Secrets, so it is possible she has been preparing us all along for Dumbledore to guide Harry through the last book via memory, gained through Harry’s inheritance of old memories and Dumbledore’s Pensieve.