Is it permissible for adoptive parents to bequeath their property to their adopted daughter, especially with no objection from the legal heirs, given her service and care for them?

If your adoptive parents bequeath to you one-third of their wealth, this is valid and becomes your property after their passing. However, a bequest of more than one-third is not valid unless the heirs approve it after the testator's death. Their approval before death is void, and they have the right to retract it. As for a gift (hiba), its validity is contingent upon the donor's legal capacity to dispose of property and your possession of the gift before any impediment arises, such as loss of capacity or death.