All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
You are not obliged to stop working during the Friday prayer because the Friday prayer is not obligatory on you. Buying and selling during the Friday prayer is forbidden for those who are obliged to perform it, as Allaah says (what means): {O you who have believed, when the call for prayer is made on Friday, then proceed to the remembrance of Allaah and leave trade. That is better for you, if you only knew.} [Quran 62:9]
As for those on whom Friday prayer is not obligatory, such as women, the sick and the travelers, as well as the non-Muslims, then they are not prevented from buying and selling after the second call of the Friday prayer is called, but you are not permitted to sell to or buy from someone on whom the Friday prayer is obligatory.
Al-Muhaththab reads, “If two men trade (at the time of the Friday prayer), and one of them is obliged to perform the Friday prayer while the other is not, then both of them are sinful, because one of them is obliged to perform this obligatory prayer and he was distracted from it, and the other preoccupied him from performing it.” [End of quote]
Allaah knows best.