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It seems that the simialar question is solved for biblatex, but I don't know how to transform my bibtex+amsrefs document into biblatex.

My question is: How to generate a citation name of \cite{test}, such that it looks like (Hilbert and Einstein, 1919, J. of Phy.), where J. of Phy. is the abbrevation of Journal of Physics.

The MME:

\documentclass{amsart}

\usepackage[abbrev, author-year]{amsrefs}
\usepackage{filecontents}
\begin{filecontents}{\jobname.bib}
@article {BHGE2017Bayesian,
    AUTHOR = {B\"{o}hm, Vanessa and Hilbert, Stefan and Greiner, Maksim and
              En\ss lin, Torsten A.},
     TITLE = {Bayesian weak lensing tomography: reconstructing the 3{D}
              large-scale distribution of matter with a lognormal prior},
   JOURNAL = {Phys. Rev. D},
  FJOURNAL = {Physical Review D},
    VOLUME = {96},
      YEAR = {2017},
    NUMBER = {12},
     PAGES = {123510, 19},
      ISSN = {2470-0010},
   MRCLASS = {85A35 (83B05)},
  MRNUMBER = {3870877},
       DOI = {10.1103/physrevd.96.123510},
       URL = {https://doi.org/10.1103/physrevd.96.123510},
}
\end{filecontents}

\begin{document}
The citation should looks like \texttt{(B\"ohm et. al, 2017, Phys. Rev, D., Thm.~3)} for the citation \cite{BHGE2017Bayesian}*{Thm.~3}.

\bibliography{\jobname}
\end{document}

The expected output: amsrefs citation with journal name

UPDATE

It turns out that if we use the label field, then the question is solved. For a test, just change the author-year option to alphabetic and replace the \bibliography{\jobname} by the following data, which is generated by bibtex except that I have add a custom label field:

\bib{BHGE2017Bayesian}{article}{
      author={B\"{o}hm, Vanessa},
      author={Hilbert, Stefan},
      author={Greiner, Maksim},
      author={En\ss~lin, Torsten~A.},
       title={Bayesian weak lensing tomography: reconstructing the 3{D}
  large-scale distribution of matter with a lognormal prior},
       label= {B\"{o}hm, 2017, Phys. Rev. D},
        date={2017},
        ISSN={2470-0010},
     journal={Phys. Rev. D},
      volume={96},
      number={12},
       pages={123510, 19},
         url={https://doi.org/10.1103/physrevd.96.123510},
      review={\MR{3870877}},
}

\end{biblist}
\end{bibdiv}

So my question can be changed as: How to automatically generate customlized label in amsrefs by bibtex. I believe the bst file (which one? since there are four:amsry, amsru, amsrs, aumrn) and amsrefs.sty is important here.

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