1. First, your mother has to give a Registered Gift Deed, gifting the shares in question, clearly specifying and indicating the Share particulars and the number of shares that is being gifted etc. and the Demat Account in which it is currently held.
2. For Gift Deed between relations, the Stamp Duty payable (Non-judicial stamp paper to be used) in West Bengal is 1/2 % of market value of the subject matter of the Gift.
3. Once the Gift Deed is so executed and registered with the Sub-Registrar's office, a request has to be sent by your Mother to the Company concerned, stating that she is holding so much number of shares, and that she has gifted the said shares to ...... vide Registered Gift Deed (copy of which is enclosed), and requesting that the said shares be transferred to the De-Mat Account, Dp-ID of the beneficiary.
4. The above is the correct procedure.
5. Instead, if your mother excutes by online Demat-Demat transfer of the shares from her Demat to your Demat, it would amount to "transfer" (not Gift) and she would be liable to pay Capital Gains Tax.