Finally I solved this problem. It had nothing to do with Forge or permissions of the storage folder. It was a minor detail related to barryvdh/laravel-dompdf,.
In the code:
PDF::loadView('pdf.quote_invoice', ['order' => $this, 'quoteOrInvoice' => 'quote'])->save(storage_path('app/quotes/Quote-') . $this->id . '.pdf');
I thought quotes folder would be created for the first time in storage/app, but it gave error:
file_put_contents(/home/forge/jrs/storage/app/quotes/quote-12391.pdf): Failed to open stream: No such file or directory
I onnected to the server via ssh and created the folder quotes in storage/app and now everything works fine.