Currently, only project IDs and names are included in the API membership listing for a user:

Project identifiers ought to be included, e.g. for allowing something like grack to authenticate access to source code repositories named after project identifiers.

The simple patch adds project identifiers to the API output.

Note that the change might break third party tools which rely on naive pattern matching of the API XML data (rather than properly parsing the XML). This should not be Redmine's concern, though.