Can the Customer, after executing agreement, by a simple letter authorize the Company to present the same for registration before registrar?

In this regard the provisions of Section 32 of the Registration Act, 1908, are relevant which read as under:

Sec. 32: Persons presenting documents for registration except in the cases mentioned in Sec. 31, 88 & 89, every document to be registered under this Act, whether such registration be compulsory or optional, shall be presented at the proper registration office:

(a) By some person executing or claiming under the same or in the case of copy of a decree or order, claiming under the decree or order there under; OR

(b) By the representative or assign of such person; OR

(c) By the Agent or representative of such persons, duly authorised by power of attorney executed and authenticated in manner mentioned.

On plain reading of the above provisions it is clear that a customer after executing an Agreement can authorize the company, by a simple letter to present the same for registration before the Registrar, as per clause (b) of section 32 of the Act. 

However, it would be advisable to obtain a registered general power of attorney executed by the purchaser in favour of the company to present the document for registration.