Protein content in sprouted beans
Short answer: 



Yes the legume seed protein content decrease when it germinates.



but still;



The sprouting seed is healthier. 



Long answer: 

Yes it is true that after germinating some of the protein decrease. It is mostly due to breakdown, transport and consumption of protein stored in seed. All fabaceae (former Leguminosae-sensu-stricto) members use a large amount of protein storage, such as Vicillins, Legumins, etc in their seed cotyledons . All edible true-pulses , including pea , mung, etc belong to fabaceae.  When the seed germinates, theses proteins breaks down into simple amino acids and small peptides, and get reallocated*.  In addition, a part of this work as food (respiratory substrate) through amino acid oxidation  **.


  Fig-1
  
  Protein mobilization in seeds... simplified.
  Source... * 
  
  Fig-2
  .
  The cellular process of protein mobilization in Mung bean cotyledon. 
  Source ... *




We are commonly advised to eat sprouting seeds not for their protein content (we get the major portion of protein from daily major foods like meat, fish, eggs, leafy vegetables, etc.); but it is for the vitamin content. 

This paper says


  " Mung bean sprout produces several kinds of hepatoprotective compounds such as flavonoid and chlorogenic acid." 


There are also many papers related to sprouting mung bean; such as this but I do not have full access to them (sorry for that), such as this, this etc.




  Reference
  
  
  * Protein Storage and Utilization in Seeds; by Rod Casey, J.Derek Bewly and John S. Greenwood. Published as a chapter in a book, Plant Metabolism, Edited by Dennis, Turpin, Lefbvre, Lyzell. Second Edition. 
  ** Amino Acid Catabolism in Plants; Tatjana M. Hildebrandt , Adriano Nunes Nesi, Wagner L. Araújo, Hans-Peter Braun (NCBI-PMC) (Full-text Free Open access link)