Ceiling fan with remote control and 2 wall switches
Unfortunately this type of ceiling fan remote isn’t made for your situation, and won’t work as you’ve described.

The remote and its receiver were created as a solution for locations where no provision was made for switching fan and light separately.  It solves a problem for those that needed to use pull-chains to provide separate controls for fan and light.

This site doesn’t do product recommendations, and I wouldn’t know which to recommend for your location anyway.  The product you desire is available tho (at least it is in the USA).  Search “fan control wall switch with remote” (I got the best results with that search, omitting “light”, however most of the products in the results also had the light control.). This product is different and manufactured to replace wall switches, allowing you to retain from the wall control as well as using a wireless remote.