Question Regarding License Conversion

Hello,

I have a problem with the driving license conversion. I started the driving license in my country and completed Theoretical test. I arrived in Germany for the first time in August 23rd 2019 on student visa and got my Aufenthalt on November 4th 2019.

I go for Holiday in my country and complete the practical test and they issue the License in January 20 2020. Which is not even 185 days of me residing in Germany.

I tried to convert my license recently since I want to buy a car but they refused. I still think they should have converted it. Anyone can help?