Is it permissible to give charity in one lump sum to a number of needy people, increasing the amount, instead of dividing it over 40 days, or must one adhere to the original intention?

It is not obligatory to give charity merely based on intention or what crosses one's mind, because the Prophet, peace and blessings be upon him, said: "Indeed, Allah has pardoned for my Ummah what they whisper to themselves, as long as they do not speak of it or act upon it." Therefore, you are not obliged to give the mentioned amount in charity as long as you did not utter any words indicating an obligation. There is no harm in giving it as a lump sum or in installments, and to one person or multiple people.