Step-by-step Solution:

\[ \textbf{Given: } \begin{cases} \text{SUN} \mapsto \text{RWK}\\[2pt] \text{MOON} \mapsto \text{LQLR} \end{cases} \] \[ \text{Find the rule: compute letter shifts (A=1,Z=26).} \] \[ \begin{array}{c|ccc} \text{SUN}\to\text{RWK} & S\to R & U\to W & N\to K\\\hline \text{Shift} & -1 & +2 & -3 \end{array} \qquad \begin{array}{c|cccc} \text{MOON}\to\text{LQLR} & M\to L & O\to Q & O\to L & N\to R\\\hline \text{Shift} & -1 & +2 & -3 & +4 \end{array} \] \[ \text{Observed pattern of shifts by position: } -1,\ +2,\ -3,\ +4,\ \ldots \] (i.e. magnitudes increase by 1 each position and signs alternate starting with \(-\) at position 1.) \[ \text{Apply to } \text{STAR}: \] \[ \begin{array}{c|cccc} \text{Position} & 1 & 2 & 3 & 4\\\hline \text{Letter} & S & T & A & R\\ \text{Shift} & -1 & +2 & -3 & +4\\ \text{Result} & R & V & X & V \end{array} \] \[ \boxed{\text{STAR} \mapsto \textbf{RVXV}} \]