Is it permissible to give the value of next month's salary as a perpetual charity on behalf of one's mother this current month, after having sworn to give it next month?

The general principle regarding an oath is that it depends on the intention of the swearer. If there is no intention, then their meaning is based on the reason for the oath. If there is neither intention nor reason, then their meaning is based on the apparent meaning of the words.

So, if you swore by one of Allah's names to give your mother from next month's salary or to give charity on her behalf, and your intention was to confirm or expedite without specifying the giving from a particular month's salary, then you can fulfill what you swore by from any salary before that.

If you had no intention, and there was a reason that led you to swear the oath, then that reason is acted upon. If there was no reason, then the apparent meaning of the words is acted upon, which means you must give her from the very next month's salary. If you do not do that, you will have broken your oath, and you will be liable for an expiation for breaking an oath: feeding ten poor persons or clothing them, or emancipating a slave. If you cannot find any of these, then fasting for three days.

As for swearing by other than Allah, it is not binding.