How to Identify a Unit of Measure From an Internal Id

Let's say that I have an item advanced search that I'm using to get information about a specific item. One of the properties I wish to retrieve is the Stock Unit. I can do this with an ItemSearchAdvanced by specifying stockUnit in search columns, under the ItemSearchRowBasic. Let's include the unitsType column as well. Like so:

 ItemSearchAdvanced advancedSearch = new ItemSearchAdvanced()  {      columns = new ItemSearchRow()      {          basic = new ItemSearchRowBasic()          {              stockUnit = new SearchColumnSelectField[] { new SearchColumnSelectField() }              unitsType = new SearchColumnSelectField[] { new SearchColumnSelectField() }          }      },      criteria...  }; 

From the search results, I can get the internal id for the Stock Unit, as well as the Units Type. In order to get the Name of the Stock Unit, it's necessary to use a UnitsTypeSearch. Using UnitsTypeSearchAdvanced with the Units Type internal id as a criteria will return search rows corresponding to the UoM, but the internal ids will all match the Units Type id, and so cannot be used to identify our Stock Unit. Instead, use a basic search: