All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In principle, according to most jurists, it isn`t permissible for a partner to take from the funds of the company except the profits of his share in the capital. However, some Shafi jurists, this also the Madhab of the Hanafi school, permitted giving the working partner a larger portion of the profits, compared to other partners, in return for his managing the company. As for the non-working partner, it isn`t permissible to give him a percentage of the profits. Al-Juaini (May Allah have mercy on him) said: "If both partners contributed equal shares of the capital but unequal amount of work and an increase was conditioned for the one who worked more, then there are two views in this regards: The more correct one is that the partner who works more is allowed to get more from the profits." {Nehayat Al-Matlab, V.7:25}.
It is stated in the book {Raad Al-Mohtaar Ala Aldur Al-Mokhtaar, V.4:311}, "In the Anan partnership of the Shafi school, it is permissible that the partners receive equal profits although their shares of the capital are unequal or to receive unequal profits although their shares of the capital are equal. However, this must be conditioned for the working partner or the partner who works more, not the non-working partner or the one who works less."
As for one of the partners receiving a specific salary against his work in the company, this wasn`t stated by any of the jurists as far as we know. However, Al-Bahooti, a Hanbali jurist, said, "It is customary practice that the working partner could bring someone to work in his place and pay that worker from the company`s funds." {Shareh Montaha al-Eradat, V.2:324}. To facilitate for the people, it is permissible to adopt the views of the scholars concerning this matter. However, the wage of the worker must be determined in coordination with the rest of the partners or their representatives as he is an employee working against a wage determined by them (Partners) or their representatives.
In conclusion, based on the details provided in the above question, it isn`t permissible to pay a salary or a percentage of the monthly profits to the non-working partner and this same ruling applies in case both partners contributed equal amounts of work or even in case one worked less than the other. And Allah the Almighty know best.