To answer your question, cutting our hair will not change the texture, though it may look like it has:

The texture of our hair is determined by the shape of the follicles (and the follicle shape is determined by our genes). Once the hair leaves our head, the texture is set. You can temporarily change the texture when chemicals, heat or a set are applied. But all these things wear off. The chemicals grow out, or the hair goes back to it's old texture when it's washed. This is because the follicles stay the same, and the hair that comes out of the follicles continues to grow in the shape determined by the follicles.

However, if your hair had a bit of curl to it, but was really long, the length can weigh down the rest of your hair, and make it look straighter than it really is. So if it's cut short, this may allow the natural wave or curl to show. So it will look like the texture has changed when it really hasn't. But when it gets long again, it will look straight once more.

Sometimes our texture changes as we age. Hair follicles can slowly change shape over time. We can get curlier, or we can even get straighter over time. This is determined by our genes. So if your follicles end up changing shape while her hair grows back, this has nothing to do with the hair cut. Nothing you do to your hair will change it permanently. Even chemicals and color grows out over time.

Texture is determined by the genes you inherited from your parents. How your hair is treated may make your texture look different, but it's still growing out the same whether it was cut or not.