A few suggestions, but some parts aren't very clear to me...
Dear Gary,
Sorry, I have forgotten to put down forgot to leave my personal email address for your reference before I left the office. This will be the email that I frequently update The address that I check most frequently is vincent@yahoo.com.sg. You can drop me an email at anytime any time.
A friendly note to inform that you that I am no longer attached with to my previous company after this contract has ended due to certain reasons now that (for various reasons) my contract has ended, and currently I am waiting for your respond for making a come back to join my lovely team and that I am currently awaiting your response to my offer to come back and rejoin my lovely team!
"Lovely team" is appropriate only if you're on very chatty and familiar terms with the recipient.
Actually, what I wrote may not make much sense. If you're waiting for his (i.e. Gary's) response to your request to have (as I understand it) your old job back, then presumably you've already contacted him about the situation and don't need to "inform" him? Or did you mean "remind" rather than "inform"? In fact, I'm thoroughly confused about what's going on (largely because I don't have the necessary background knowledge, rather than because your letter is particularly confusing in itself). I don't understand the relationship between the company whose office you just left, BAT, the company you call "my previous company", and the company you later call "my company". I don't understand which of these are different and which (if any) are the same, or who Gary is and how he fits into this setup. So, some of my suggestions may not be appropriate!
If you lend a hand in negotiation negotiating my charges to be pushed up to RM 500 per day, in this case I will assure you to further pursue commit to pursuing my BW Certification at my own expense without the need of for BAT subsidizing to subsidize it. By doing so, it This will bring you the further benefits of having benefit of a strong technical person in your support team to serve the team for betterment and also for the organization.
To accelerate the process, I will proceed go to the registration center tomorrow for to arrange my company’s registration, & and I will pass to directly Gaya this directly to Gaya once your side has been settled.
I understand it will take for a while for BAT to process in order to settle my agreement agree and process my contract [??]. For all that said, I really want to thank you again for your time & and your helping hand help. I do appreciate it, and I am looking forward to hearing from your good news some good news from you!