Answer
$t = 4.00~years$
Work Step by Step
We can measure the length of the armada according to an observer in the ground frame $S$:
$L = L_0~\sqrt{1-\beta^2}$
$L = (1.00~ly)~\sqrt{1-(0.800~c/c)^2}$
$L = 0.600~ly$
The relative speed of the messenger compared to the armada is $0.150~c$
We can find the required time:
$t = \frac{0.600~ly}{0.150~c} = 4.00~years$
