Hi Bruno,
yes you can instruct the solver to store this file. You can do so by setting the project option "Solver Listing Messages" (under Solvers general options) to the value "All".
This will create a status file in the log directory for the solver you are using (e.g. cplex 12.5.sta).
Note that most solvers also have some possibilities to modify what exactly is logged. For example, when solving MIP problems with CPLEX, you can set the CPLEX option "mip display" to "Nth node + LP display for root node" and the "mip interval" to 1 to get a full log of the MIP solving process as done by cplex.
Please see the help of the different options for more information.
Guido Diepen
AIMMS Specialist