Can an employer fight unemployment benefits if they gave the employee a promotion a week before?

Salaried employee was fired from Akron based company after 5+ years of work. At time of firing, Employer gave Employee letter outlining reasons for firing which were minimal infractions at best (e.g. late response to email).

Employee received no warnings or disciplinary measures about the infractions and, in fact, was promoted a week prior to the firing. The infractions were to have occurred prior to the promotion.

Employer offered no severance and stated they would fight unemployment benefits.

Because of the recent promotion and minimal infractions, does the Employee have sufficient grounds to fight the Employer if they try to fight unemployment benefits?