First, of all not provided the appointment letter is made situation as tricky & diplomatic, it can be use by double edge from both side (Employer as well as employee also.). it will be treated as he is not aware about the terms & condition of your company & employment, then how can you take action against him...? as well as if he didn't signed the letter therefore, there is nothing any employer & employee relationship with you. but, it is very daisy situation, it be overlap on you (Employer) also.
Secondly, Absconding letter can be issued only on not reporting to duty without any intimation. but, in this case, as i believe, he is coming to office or report to duty but, doesn't follow the company process & rules.
Thirdly, Employer has reserved rights to terminate the service during the probation period subject to follow the certain rule & valid reason, as probation is giving for such purpose that, after hiring, you need to understand that, whether the selected person is suitable for your organization or can he perform well or not..? on that basis his employment can be confirm.
Even though, termination of employee during the probation period or post probation is proscribed in " The Bombay Shops & Establishment Act.(As i believe this act. is applicable to you) Section 66: Notice of termination of service:-
No employer shall dispense with the services of an employee who has been in his [continuous employment] -a) for not less than a year, without giving such person at least thirty days notice in writing, or wages in lieu of such notice:b) for less than a year but more than three months, without giving such person at least fourteen days notice in writing, or wages in lieu of such notice: c) Provided that such notice shall not be necessary where the services of such employees are dispensed with for misconduct. [Explanation-For the purposes of this section, "misconduct" shall include-a) absence from service without notice in writing or without sufficient reasons for seven days or more;
b) going on or abetting a strike in contravention of any law for the time being in force; and c) causing damage to the property of his employer.
Therefore, i would advise you that, by give him the appropriate notice as mentioned above for termination of his services further.
23rd July 2014 From India, Mumbai