Help with replacing tabs inside "" with some text/blank

Shell Programming and Scripting
1

I am poor with scripting;)

I have a file in the following format;

'This is a "test in production" of importance.'

I want to get rid of the spaces inside the "" part only to get the output as,

'This is a "testinproduction" of importance.'

2 
 awk 'BEGIN{FS=OFS="\""}{gsub(" ","", $2)}1' file

Regards