The strengths of Gamow-Teller transitions $B$(GT) and their summed values $\sum B$(GT) have been investigated for the transitions $^{9}$Li$\rightarrow$$^{9}$Be, $^{9}$Be$\rightarrow$$^{9}$B, and $^{9}$C$\rightarrow$$^{9}$B in the framework of the shell model.~The calculations were conducted in the standard P and extended PSD model spaces with core taken at $^{4}$He with effective interactions $ckpot$ for P model space and $psdmk$ and $psdmwk$ for PSD model space.~We did not impose any restrictions in our calculations for both model spaces.~The calculations of $B$(GT) for the studied nuclei and their summed values $\sum B$(GT) were compared with the observed data and shows reasonable agreement.~We have obtained a qualitative agreement for the individual transformations, and the observed and measured total transformation strengths are quite similar.