Circular Convolution as Cyclic Shift Operator
You may solve it by 3 steps:

Show yourself that a Cyclic Convolution with a vector $ \boldsymbol{e}_{i}^{N} $ is a Cyclic Shift Operator $ {T}_{i - 1} \left( \cdot \right) $. Where $ \boldsymbol{e}_{i}^{N} $ is defined as a vector of length $ N $ which all its elements is zero but the $ i $- th element which is 1.
Decompose $ \phi $ into $ 3 $ vectors of type $ \boldsymbol{e}_{i}^{2 N} $.
Use linearity of the Cyclic Convolution to prove your assertion.