All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If the sister who passed away did not leave behind except the heirs that were mentioned in the question, then the inheritance should be divided as follows:
The mother gets one-sixth part of the inheritance and the rest will be for the father. The brothers and sisters do not get anything because of the existence of the father and this is according to the consensus of the scholars . So the mother gets one-sixth of the sum of Egyptian pounds which is 5212,67 and the rest will be for the father and that is 26063,33 Egyptian pounds. Also, the mother gets one-sixth of the weight of gold, or the equivalent of 2580,83 Egyptian pounds and the remainder is for the father which is 12904,17 Egyptian pounds.
As regards the saying of the father that his share is for his children, then he is permitted to gift his share to his children while he is still alive but he is obliged to be just between them in his gift as the Prophet said: "Fear Allaah and be just between your children."
But is it justice that he should divide his share equally between them or that he should divide the share of the male to be twice that of the female? The majority of scholars are of the view that he should divide it equally between them. However, the Hanbali School of jurisprudence is of the view that he should divide it amongst them according to the Book of Allaah, the portion of the male is twice that of the female.
Anyway, this is an easy matter and the father can choose either possibility and should act according to the benefit of all so that no one would have any hard feelings towards the other.
What you have been told that the brothers and sisters will get one-third part of the inheritance is not correct because the brothers and sisters do not inherit due to the existence of the father. The Prophet said: "Give the prescribed share of inheritance to those who are liable for it and the remainder [of it] is for the nearest male relative." [Al-Bukhari and Muslim]
Finally, we like to remind you, dear brother, that dividing the inheritance is very complex a matter as it is about people's rights, so a mere Fatwa which is an answer according to the question is not enough in this regard. Rather, it is more appropriate to take the case to an Islamic court to look into the matter and to make sure about everything as it might be that there are some rights before the share of the heirs, like debts, or a will and the like. There could be also an heir that is forgotten and who could only be found after investigating the matter. Therefore, this inheritance should not be divided before resorting to an Islamic court.
Allaah Knows best.