Praise be to Allah.
Acceptance of gifts by employees to finish paperwork is bribery
Employees and civil servants should fear Allah, may He be exalted, with regard to their work, and they should do their work in the manner that is required of them, without any delay or falling short.
It is not permissible for them to accept gifts from clients or those who need to have paperwork done. It is forbidden for them to delay doing the paperwork and not complete it except in return for money that they receive.
They should know that it is haram for them to consume this wealth or feed their children with it , and it comes under the heading of bribery , for which the Prophet (blessings and peace of Allah be upon him) cursed the one who accepts it.
‘Abdullah ibn ‘Amr ibn al-‘As (may Allah be pleased with him) said: The Prophet (blessings and peace of Allah be upon him) cursed the one who gives a bribe and the one who accepts it. (Narrated and classed as sahih by at-Tirmidhi (1337). Also narrated by Abu Dawud (3580) and Ibn Majah (2313); classed as sahih by al-Albani in Sunan Abi Dawud)
Shaykh Muhammad ibn Salih al-‘Uthaymin (may Allah have mercy on him) said:
“It is not permissible for any employee in any government department to accept gifts for doing paperwork connected to this department, because if we open this door and say that it is permissible for the employee to accept this gift, we will have opened the door to bribery. Bribery is a very serious matter, for it is a major sin. Therefore what employees must do if they are given gifts having to do with their work is return these gifts, and it is not permissible for them to accept them, whether they are called gifts, charity, or zakah, especially if they are rich, for it is not permissible for them to accept zakah, as is well known.” (Fatawa Ibn ‘Uthaymin, 18/359-360)
Is giving money to finish paperwork bribery?
It is also haram for employees to accept bribes, and that is also haram for the giver to give, unless he is compelled to do that for fear that there will be some delay or other problem with his paperwork that will lead to loss or harm. In that case, the sin will be on the one who accepts a bribe, not the one who gives it, on condition that the one who needs to have his paperwork done is only doing that in order to attain what is his due.
Ibn al-Athir (may Allah have mercy on him) said:
“With regard to what is given in order to be able to take what is one’s due or to ward off injustice, that is not included in the prohibition on bribes.” (An-Nihayah, 2/226)
Al-Khattabi (may Allah have mercy on him) said:
“If he gives [something] in order to attain what is his due or to ward off injustice from himself, then that is not included in this warning.” (Ma'alim al-Sunan, 5/207)
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
“It is permissible for the giver to give whatever will enable him to take what is his due or ward off injustice from himself. This is what was narrated from the early generations (salaf) and leading scholars.” (Majmu‘ al-Fatawa, 31/287)
This has also been discussed previously in the answer to question no. 72268 .
And Allah knows best.