Google Analytics attributes the conversion to the last source that the visitor used right before converting. However this default behavior can be overridden if you want to attribute to the previous campaign rather than the most current one. In order to do so you have to pass in an additional parameter utm_override=1 in your campaign URL
Conversion from a visitor who comes via clicking on the above URL will be attributed to the previous source that the visitors came from instead of the above campaign.
Note: If you omit utm_nooverride=1 in your next campaign and the same visitor comes back again from the new campaign and converts then the conversion will be attributed to the this new campaign.