How can I change the names of my supplementary tables and figures from "Figure S1" to "S1 Figure"?

Question

I've been writing a paper in LaTeX which includes supplementary information, containing supplementary tables and figures.

I used this command:

\newcommand{\beginsupplement}{%
        \setcounter{table}{0}
        \renewcommand{\thetable}{S\arabic{table}}%
        \setcounter{figure}{0}
        \renewcommand{\thefigure}{S\arabic{figure}}%
     }

The result is that all the tables and figures are referenced in the text as "Figure S1", "Table S2", etc.

Because of the journal requirements, I've to reference to them as "S1 Figure", "S2 Table", etc.

How can I do it?

Thanks

EDIT: I am referencing all the citations in the paper through the \autoref{} command. I also have another request from the journal editors: I should use this new notation ("S1 Fig.", "S2 Table", ) also in the captions of the figures and of the tables themselves.

I have to change the caption from Figure S1 from "Figure S1" to "S1 Fig.". I have to change the caption from Table S2 from "Table S2" to "S2 Table". How can I do it? Thanks