Yes, you can provide appointment letter to person who is placed at B company. This is because, it is your company's responsibility to provide training to the persons of Company B. Thus, you are fulfilling your responsibility by sending your person to the premises of Company B for the purpose of providing training.
Also you can mention that the person is from Company A in the said letter.
You also need to check the factors like who is going to give salary to him. Who will be contributing for PF, ESIC etc of this person who will be at Company B. Generally, the Company, who is going to pay salary and do the statutory compliance, should ideally issue him an appointment letter.
Adv. Manish Gadre
16th July 2019 From India, Mumbai