Bismillah,

الجواب وبالله التوفيق
As per the situation described in your question, the wife will have to bring proof to substantiate her claim that the husband has issued the third divorce. If she is unable to produce such evidence or proof, the third divorce will not take effect. However the wife in this situation should not let the husband take power over her (i.e. do not let the marital relations be established).
If the second marriage has in fact taken place and the report regarding it is true, then due to the fulfillment of the condition for the conditional divorce, the divorce will take effect. If however, if there is no proof or substantiation of the claim of this second marriage, then due to the nonexistence of the fulfillment of the condition, the divorce will not take effect.
واللہ اعلم بالصواب
