Let us say that there is a unique solution for a given set of parameters (around a large enough neighborhood).
It can be be the case that some of the algorithms available with the perfect foresight simulation in Dynare are more equipped to actually find the solution. Other algorithms might deviate from the solution. It might depend on the behavior of the model.

What are you saying is, if two algorithms converge, and there is a unique solution, then they will all converge to the same solution. The only difference is that some might take longer to reach the solution.

Moreover, if there is a unique solution, usually stack_solve_algo=0,robust_lin_solve
will more likely find the solution.
Are these two statements right? Thank you