I dont know if that mockup i similar to yak-44. Besides, the problem with buying the yak-44 design is that it never left the mockup stage. After all this time, there shouldnt be much left from that program. Also russia wouldnt be too keen in selling it to china.
Well the Russian did most of the work already even if it still in mockup stage. China receive a SU 33 prototype from Ukraine and they based J15 on that prototype
An unfinished Su-33 prototype, the T-10K-3, was acquired from in 2001 and is said to have been studied extensively, with development on the J-15 beginning immediately afterward
So it is not worth ed spending money and manpower to built just 4 or 5 planes
And AVIC did work closely with YAK design office and JL15 look very similar to Yak 130
So who know if the price is right Yakovlev design office might sell the preliminary design of YAK 44
China did use the service of Kamov to do the preliminary design of Z10. So nothing is impossible now that China and Russia are strategic partner