Just extract the solution at 1 s from s (i.e. the last row in s). Then simly run the integration from there:
t2 = linspace(1,3,2001); % or what resoution you need
s0_2 = s(end,:); %
[t1to3 s1to3] = ode15s(@(t,s) fun(t,s), t2 , s0_2 ,options);
That should be enough.
HTH
