How to say "If you would like to know any updates , you can always call or message me"

Question

According to my understanding, “update” is translated to “更新” . But this seems to be in the context of Software。 Eg. Software update, OS update ,etc. But how would you convey update in the following scenario : There is a customer who wants to do online trading. He has submitted some documents which need to be checked,translated and verified before he starts trading. The whole process may take up to 4 days. The customer needs to be told that if there's an update , he will be informed by mail. Also, if he wants an update as to where the process has reached, he can send a text or a mail. In this scenario, how do we accurately convey the message with or without using the translation for "Update" ?
One way I thought could be using 流程有事的话我会通知您。您有问题的话也您通过微信或邮件跟我联系. Any suggestions or alternatives ?

Answer 1

如果您想要了解后续进展的话，可以随时电话或邮件联系我。

Toosky Hierot's comment ”欲获知后续进展如何“ sounds a bit too literary to me. I think "如果您想要了解后续进展的话" is a more common way to say it, though I agree 进展 or 后续进展 is the right word choice here