你的选取的只是一小段，缺少必要的前后语境，我帮你从网上找到这篇文章，还附有翻译，对于理解很有帮助（下面的引文和翻译来自网络）：

The Morning Report 晨间家书

Sometimes he slips in cryptic teaser. For example, recently he told us, “I’ve climbed halfway up Mount Washington!” Given his age and distance from New Hampshire, such a hike was unlikely. I was befuddled for a day or two until he reminded me he was working on a hooked rug with a scene of the mountain.

有时候父亲也会突然开个玩笑。譬如最近，他告诉我们“华盛顿山我爬完一半了！”以他的高龄，再考虑到西部距新罕布什尔州华盛顿山之间的距离，这么一次远足应该是不可能的。我还为此困惑了好几天，直到有一天，他告诉我他正在钩织一条带华盛顿山图案的地毯，我才恍然大悟。

Each e-mail closes with “All my love, Dad.” When my mother was alive, that sentiment was normally reserved for her. Now that she is gone, he shares those feelings and his experiences with us. For me, what started as a simple security measure has spawned a deeper closeness.

父亲的每封邮件都以“爱你们，爸爸”结尾。母亲在世时，这份柔情都是倾诉给她的。现在母亲走了，父亲就和我们分享他的感受与体验。对我来说，晨间家书原本是为了确保父亲的起居安全，现在使我们和父亲的关系变得愈加亲近了。

I’m grateful my father is still able to manage his computer and the Internet. I know the day will come when he’ll no longer be able to write the reports, and we’ll have to find other ways to keep tabs on one another. But until then they are our way of knowing that another normal day has begun.

我很庆幸，父亲现在还能使用电脑和互联网。我也知道，终有一天，他再也不能写晨间家书了，我们得另寻其他的办法来保持彼此间的联系。在此之前，晨间家书让我们知道，又一个日子刚刚开始，安好无恙。

你的句子中的 until 相当于 before，这里的 until then 相当于 before that（在此之前）。这里 begin 用现在完成时态，和 until 没有关系，属于现在完成表示影响的通常用法。这里用现在完成时只是表示表明新一天已经开始，知道父亲“安好无恙”（指每天看到父亲的 report，就知道他“安好无恙”，这样作为子心里的一块石头也就暂时落地）。