[It is permissible for the rightful owner to give a bribe in order to obtain his right(2)]

Answer – and Allah is the One who grants success: If the right that is sought to be obtained by means of the bribe is definitive (qaṭʿī), then it is permissible to obtain and ransom it by means of a bribe. By our saying “definitive” we mean that the one giving the bribe knows, with necessary certain knowledge that admits of no doubt, that the disputed right is his property, or he knows that he has a stronger claim to it than anyone else – such as a share of inheritance or the like. For what the deceased left behind is, apparently, what had been his property. This is on condition that there is no one disputing the estate of the deceased or any part of it.
But if the disputed right is not as we have described, then bribery is not permissible, because it is possible that the right belongs to someone else – namely, the other party. And this is due to His saying, Exalted is He: “And do not consume one another’s wealth unjustly, nor deliberately bribe authorities in order to devour a portion of others’ property, knowing that it is a sin.” [Al-Baqarah:188]. From this verse, the evidence is also derived for the first category, which is the permissibility of bribery to extract a known, established right.
The aspect of the verse’s indication to what we have said is that His saying, Exalted is He: “and [do not] send it [in bribery] to the rulers” is conjoined to “do not consume”; thus, it falls within the scope of the prohibition. It has been established among the people of knowledge that the prohibition is directed to the qualifying clause. His saying, Exalted is He: “in order that you may consume a portion of the wealth of the people in sin” is a qualifier of the prohibited act, which is: “send it [in bribery].”
On that basis, giving money (to the rulers) is not prohibited except when it occurs in this manner.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.2