Different contributor here. Please permit me to assist.
Cal. Labor Code 2922 provides that an employer can terminate the employment relationship "at will": at any time, for any reason, or for no reason at all. There are several exceptions to this rule, one of which is that where an employee handbook or other written employer policy requires certain disciplinary rules, and the employer does not follow its own rules, then the employer breaches its contract with the employee, and the employee has a claim for damages based upon the breach -- in the amount of lost wages until the employee finds new employment (or, at the employer's choice, until the employer reinstates the employee).
What this all boils down to is that you must be able to show that you were entitled to purchase furniture at a discount and that there were no restrictions on where it could be delivered or who could sign for the purchase. You would also have to show that the employer has a written policy that requires certain steps must be followed before employee termination, and that you were not afforded those steps. Otherwise, the claims of fraud and/or forgery, while clearly outrageous, are actually irrelevant -- because as previously mentioned, Labor Code 2922 permits the employer to fire you without any reason at all. So, the employer can rattle on about anything it wants to as a rationale for terminating you, but none of it actually matters.
What matters is: (1) there was no policy prohibiting your actions, re the discount purchase, and (2) you were not afforded the steps required to be followed by the employer prior to terminating your employment. If you can prove both, you can win a court action against the employer -- and probably force a settlement. Otherwise, your only recourse is to file an unemployment insurance benefit claim and move on to find a new job.
Note: Assuming you can prove your claim, you could sue in small claims court for up to $10,000 in lost wages -- without hiring a lawyer. Otherwise, you will need an employment rights lawyer. For a competent referral, see this link
Please let me know if I can be of further assistance.