Is it permissible to give my sister an embellished pair of shoes, knowing that she will wear them in public, with my intention to advise her later?

The permissibility of gifting embellished shoes to your sister depends on the degree of their embellishment. If the adornment attracts the attention of men, then it is not permissible to wear them out in public. However, it is permissible to gift them to her to wear inside her home or only in front of other women. But if you predominantly believe she will wear them outside, then it is not permissible to gift them, as they would be a means to sin. If, however, the embellishment is subtle and does not attract attention, then there is no harm in gifting them and wearing them out.