This is the problem of interpolation from low to high resolution of grid data. Formally this can be done, but there is question of the size of the error? I suggest you try different functions, so consider what is the most acceptable.
Generally it is hard to do interpolation from coarse to fine temporal resolution, specifically for the variables that have larger seasonal dynamics, such as temperature, soil moisture...... So as Milivoj said, please consider more acceptable approaches.
The process of converting annual data into monthly data is an illogical process because we will lose accuracy in measurement, which increases the amount of error, except in the event that seasonal indicators are available to follow the monthly behavior of the apparent, otherwise, I cannot adopt it as a realistic application, but it is just a mathematical function.
If you convert yearly data to monthly by using any techniques. It involves error. So take care about it. There is lots of mathematical techniques to find such type of intermediate values like Interpolation or least square method but problem is the same "error" that involved in this process.