Praise be to Allah.
We ask Allaah to reward you with good for your desire to treat your wife’s mother kindly and to bring your wife close to her family, and for the travelling, moving and giving up work that you are putting up with for this purpose.
What you have done – signing for the days when you are absent from work – is undoubtedly a haraam action, because it involves lying and consuming people’s wealth unlawfully. Allaah says (interpretation of the meaning):
“O you who believe! Eat not up your property among yourselves unjustly”
And the Prophet (peace and blessings of Allaah be upon him) said: “Truthfulness leads to righteousness and righteousness leads to Paradise. A man will keep speaking the truth and striving to speak the truth until he will be recorded with Allaah as a siddeeq (speaker of the truth). Lying leads to immorality and immorality leads to Hellfire. A man will keep telling lies and striving to tell lies until he is recorded with Allaah as a liar.” Narrated by al-Bukhaari, 5629; Muslim, 4719.
The salary that you have taken in return for these days should be given back to your workplace; it is not permissible for you to keep it because it is haraam wealth. The Prophet (peace and blessings of Allaah be upon him) said: “Every body that is nourished with haraam food, the Fire is more fitting for it.” Narrated by al-Tabaraani from Abu Bakr; classed as saheeh by al-Albaani in Saheeh al-Jaami, 4519.
Al-Tirmidhi (614) narrated from the hadeeth of Ka’b ibn ‘Ajzah: “There is no flesh that grows from haraam food but the Fire is most suited for it.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
You have no right to give this money in charity, because wealth can only be given in charity when its owner is unknown or it is too difficult to reach him.
It is not permissible for you to carry on being absent from work whilst signing in as present. You should look for a way out that will not involve sin, or you should agree to take early retirement now, without getting the incentive of the lump sum that you mentioned. Remember that that which is with Allaah can only be attained by obeying Him, and that haraam wealth erases blessings and will bring evil consqeuences in this world and in the Hereafter.
This advice was offered by Shaykh Ibn Baaz (may Allaah have mercy on him) to the one who was careless about his attendance at work, and was not honest in recording the times when he was present. He (may Allaah have mercy on him) said: “It is a duty for every Muslim to fulfil his trusts and to beware of cheating at work with regard to attendance and absence and in all matters. What he must do is to record the time when he entered and the time when he left, so that he will have discharged his duty. The boss has to advise them sincerely and direct them to do that which is good, and warn them against cheating. And Allaah is the Source of strength. End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz, 19/356.
We ask Allaah to guide us and you.
And Allaah knows best.