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Unfortunately no. The witness has to sign it in front of the testator: "Witnesses’ signatures.—The attesting witnesses must sign the will in the presence of the testator and in the presence of each other." 732.502(c) FL Stat. Probate Code.
Since you offered Father's will for probate and it was rejected, and there is no previous properly executed will, then you would proceed as if your Father had no Will. So, since your Mom died after him, technically, she would have most likely inherited something from him.. Therefore, you would have to have two proceedings, one for your Father, and then one for your Mother. Possibly the court clerk can help with a way around this. But you would start with your Father's first. Since you are the only child left, you would have a share, and possibly your brother's children depending on the dates of death.