Question: a problem of subs

Hello people in mapleprimes,

I want to modify the next equation: 

(**)  a:=sigma*omega*alpha = mu(H, H)*s*omega*gamma1*L+mu(F, H)*s*L-mu(F, H)*s*L*gamma1;

to be

(***)    sigma*omega*alpha = mu(H, H)*s*omega*gamma1*L+(1-gamma1)*mu(F, H)*s*L;

For that, first I defined b as

b:=sum(op(k,rhs(a)),k=2..3)=collect(sum(op(k,rhs(a)),k=2..3),{s,L,mu(F,H)});

, and substituted this to a with

subs(b,a);

But, what I could obtain was only the orignal equation (**) not (***).

Please tell me how to use subs to this problem to obtain (***)。

Thanks in advance.

taro

P.S.

I know

(****)collect(lhs(a)=rhs(a),{s,L,mu(F,H)});

works well as for what I wrote (**) as above.

But, originally, it was a result from substituting various equations into an equation.

For it, (****) does not work well.