Your TE44 utilizes the T-31 turbine wheel. They should be able to upgrade your turbo to a 6157 and depending on the condition of your bearing housing, turbine wheel and turbine housing, should be able to be done.
You would be paying for a new compressor wheel, compressor cover, backing plate, clamps, bolts, o-ring, internal bearing housing components and the labor if the rest of your parts were reusable. They would definitely need to do a tear down inspection to see what you have to work with first tho.
But the answer is yes, they should be able to upgrade your turbo.
HTH
Patrick