Dear forum experts, in a previous thread, I mentioned that I was counseled out and applied to many firms when I was still with the firm. Experts suggested that I shouldn't disclose that I have left the firm in interviews unless being directly asked. 

In recent interviews, I have followed this path, only mentioning I want to switch jobs due to motivation reasons. Now that I have left the firm, I'm wondering if the interviews takes a long period (2-3 months), can I still follow the same strategy and conceal that I have already left?

Assuming that I received an offer 2 months after I left the firm, the HR would easily find out that I have left the firm when I provide my proof of employment which states the last employment date. (Also, when interviewing with firms, people might “gossip” and reach out to my previous firms' staffs, and may find out that I've already left.) Would it be a big issue when the HR finds out that I have already left the firm a while ago, but chose not to disclose?

Highly appreciate your thoughts.