Can hair texture be changed by theoretically transplanting hair from one person to another? (Photo)

You can't transplant another person's hair to your scalp. Unless you they are your identical twin.  Otherwise, your body will reject it.

Hair texture is determined by genetics. And DNA governs the
shape of the follicle and how the hair is produced within these structures.

Follicles cannot be transferred from a different person. The
only exception would be in the case of identical twins. However, they would
have the same hair texture. Theoretically, if follicles could be safely and reliable
transferred from other people, the hair would maintain its original texture due
to the DNA codes which reside in the cells of these structures.

Every person has a different protein signature. And this
would trigger a response from your immune system. This would involve an
aggressive attack on the follicles since the immune system recognizes them as
being foreign to the body. Therefore the grafts would not survive.

Immunosuppressant drugs would create additional
complications and lower your body’s defense, making you vulnerable to various
diseases and infections. 

It is not possible to transfer one person's hair to another. The body will absolutely reject the foreign hair.

You are correct that it is not possible to transplant hair from one person to another. But if it was (theoretically) the transplanted hair would indeed take on most of the characteristics of the "donor" hair. We call this phenomenon donor dominance. Although never tested, I suspect the donor hair would lose a bit of its curl over time.

This should never be done unless the donor is an identical twin. Hair from another person will reject just like a kidney or heart transplant unless treated with powerful drugs after the surgery

Texture can be changed if the texture is different in each individual.  The transplanted hair will keep its original intrinsic characteristics.

Yes if the hair could be transplanted from a straight haired individual to a curly haired individual the donor hair would keep its original character. However this is ABSOLUTELY not possible (one individual to another individual) and probably will not be for years to come.