"But you still don't answer my question, what are the objectives of the US and Britain and additionally, what is their follow-up plan if they were achieve them? "
I did answer that: I said that they probably don't have a plan. And that I was unsure whether that was a good or a bad thing, given the sort of "plan" that Putin has.
I also said that the "west" (US and Britain if you like but others too) are condemned by their own side either:
By the conspiracy theorists who say that the whole thing is a CIA plot and that there is a machiavellian plan somewhere deep in Langley being slowly carried out,
By those who say we're all pathetic for not having a plan at all, compared to Mr Putin and his angels of death
And several shades in between.
The best plan for Syria is the one that stops the fighting between the rebels and the regime. But no one has one of those as far as I know.
Meanwhile, IS is about to be driven out of Mosul in Iraq, and the war against them will continue, spearheaded as it is being at the moment, by western and ME allies.