I have just imported my PLS standardized LV scores in SPSS (wanted to check VIF) and run a regression.
Results: I have the same standardized coefficients in the 2 models (which is normal) BUT I have different p values for some coefficients (lower p values in SPSS compared to PLS). For instance, one variable has a p value of 0.08 in PLS and 0.01 in SPSS.
A precision: I have 637 observations.
I guess the differences come from the fact that the significances (t-values) in PLS is estimated with bootstrap, for this reason it is "distribution free".