$DFA/NFA$ for $L(OPPOSITE)=\{uv:vu\in L\}$

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I'm trying to prove that: $L(OPPOSITE)=\{uv:vu\in L\} \in L_{FA}$ given that: $L \in L_{FA}$ . I'm trying to construct a finite automata that accepts $L(OPPOSITE)$ in order to prove it but I got stuck. Any help will be greatly appreciated!