I have a collection box for one of the charities, and once it is filled with money I want to give it to a different charity which I believe to be more trustworthy.

Praise be to Allaah. 

We
put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may
Allaah preserve him, who responded by asking,

 “Why
did he agree to keep a box for this charity?”

 (We
said:) Because it was the charity that he knew of, then he found another
that is more trustworthy.

 (He
said:) It is not permissible. So long as he collected the money with the
intention of giving it to the first charity, it is not permissible for him
to give it to another.