Simple application of Donsker's theorem

Question

I am trying to do exercise 5.15 in Moerter's book "Brownian Motion". It seems quite easy, but I can't solve it somehow: Suppose $S(j)_j$ is a SRW on the integers, started at zero. Show that: $$ \frac{1}{n^2}\min_j\{|S(j)|=n\}\to^d\min_t\{|B(t)|=1\}\, . $$ Now, this looks like a standard application of Donsker's theorem (although, perhaps it is not?). Anyway, I tried hitting it with Donskers theorem, but I just keep getting nonesense: $$ P(\min_t\{|B(t)|=1\}\le s)=P(M_s\ge 1)=P(B\in K_s)\, \ $$ where $M$ is the max of the modulus of a Brownian motion and and $K_s$ is the set of continuous functions whos maximum is bigger than one. But: $$ P(S^*(t)\in K_s)=? $$ The first problem is that we don't have the intervall $[0,1]$ as required in Donsker's theorem, and the second one is that I cannot related the interpolated and scaled SRW to the property above (the one with $1/n^2$) Any help welcomed. thank you!