The mode of written communication within company provided to employee is by email. The reliving issued by business head should suffice. The employee is not at fault, if HR is not kept in loop by the issuing authority. The employee shall not now resign from current employment and serve the balance notice period and hunt for job again or tender notice pay and message the inflated ego of lady in HR. If the business head is not relieving authority or if HR is issuing authority then the rules in this regards should have been circulated to employee in writing. The episode is nothing but tussle for supremacy of HR in which hapless employee is getting harassed.
You can submit a representation by letter under acknowledgment to the good offices of appointing authority, MD, Head-HR, Company secretary and highlight that you were relieved by not by just anybody but business head and after that only you entered into your future venture and now you would like to focus on your current source of livelihood.
As a good employee you have applied for and obtained proper reliving. Instead of separating at a good note why unnecessarily you are being bothered and a strain is being caused on your current source of livelihood by Ms..............
You can also seek an appointment with the good offices and clear your stand and demand relief. Kindly submit the minutes after the meeting.
Other situation is that your business head has obliged you and now you should apply your rapport, goodwill, negotiation, persuasion, reasoning skills to manage the situation in your favor by talking out the matter with HR and good offices without letting the issue complicate.
If nothing works you can lodge complaint with local o/o labor commissioner.