Is it permissible to have intercourse with one's wife before Ramadan if she has not been able to make up all the days she missed in the previous Ramadan, knowing that she sought her husband's permission to fast and he granted it?

It is not permissible to break a compulsory fast, such as making up for missed Ramadan days, except for a valid excuse. Whoever breaks the fast, whether with or without an excuse, must fast a day in its place. If the fast was broken without an excuse, repentance is obligatory. There is no expiation (kaffara) on the wife because expiation is only required for sexual intercourse during the daytime in Ramadan. You have erred by spoiling your wife's fast, and both of you must repent. If you forced her, then there is no sin upon her.