First ask around with the other employees to find out if he's treating any others the same way. If you're certain that all the others are being kept better informed, then your on more solid ground.
Then you could just tell him what you've noticed.
It would need to be framed tactfully.
"There've been several occasions when I haven't received important information and haven't received notice of meeting till the last minute. (Have a list of all the occasions with you. If he asks name at least one of each and then give him your copy of the list.) Also I've noticed that this is not the case for the others who work here."
I feel frustrated because this makes it hard to be well prepared and do my job to the best of my ability.
I would really appreciate it if you'd let me know meeting times and important info as soon as you have it."
And then wait for his answer. Be ready to negotiate. He might have specific needs that you might be able to help with.
If the direct approach doesn't work...
would it be possible to ask him out for lunch or a cup of coffee? Preferably just the two of you. Start with re-establishing the feeling of friendship. How are things going at (his) home? en you could ask him how things are for him at work. What are his plans?? What will he be doing after you move into his job? How does he feel about it
That might be an easier way to explore what's going on.
If it seems that he does have a motive for sabotage, it will take some subtlety and tact to find out what's really going on because he won't want to tell the truth about it - and he'd be unlikely to want to stop.
If his motive is unrealistic - merely paranoia - you might be able to put him at his ease by showing him that you're willing and able to support him in his goals for the company. All you would need to know is what kind of support he needs.
If none of the above works, you may need to resort to being underhanded yourself. Find out who's getting the important emails and notifications first and ask them to forward the info to you instantly. Ask them all so there's a guarantee that you'll get it.
Wishing you all the best.