«إِنْ أَخْبَرْتَنِي بِقُدُومِ فُلَانٍ فَأَنْتَ حُرٌّ»
“If you inform me of so-and-so’s arrival, you are free.”
Ba attaches the report to the actual arrival being reported. The truth of the information therefore matters in assessing whether the condition is met. A false report is not equivalent to a truthful announcement of an arrival that took place.
By contrast, “if you tell me that so-and-so has arrived” can make the act of reporting more independent of whether the content is true. The difference in wording may affect fulfilment of the condition.