Dear Nayak,
They have transfered you to their company and also they have not taken any resignation from you, this act itself makes your employment continious. In one judgement of madras high court namely Mettur beardsell Ltd. Case it was the same ration given by The Honb'le Justice Abdul Wahab. Also for the purpose of payrolling they will have to give you joining letter that dosen't make your employment afresh. So focus on your work and throw all your worries out of window, leave these this for the time when you leave this organization and if at that time they decline you to give gratuity for the period you worked for the sister concern, you file a complaint before Assistant Labour Commissioner on the basis of that transfer letter. However please keep that transfer letter safe till that period.
Hope that clears all the doubts. feel free to revert in case of any further clarification.