Here are the posts (from the copies which were sent to my email):
wa 'alaykumus-salāmu wa rahmatullaahi wa barakaatuh
The ḥadīth of the prayer after using siwaak (miswaak) being better than prayer without it by 70 times has been reported with chains to a number of companions, all of them with weak chains, with the exception of one apparently hasan chain from the book "as-Siwaak" by Abū Nu'aym. This book had dozens of supporting narrations for this ḥadīth, but the book has been lost. However, some of those chains have been quoted along with their wordings in two important books, "al-Imām" of Ibn Daqeeqil-'Eed and "al-Badr al-Muneer" of Ibn al-Mulaqqin. There is a strong argument for someone to say the ḥadīth is established by way of its numerous routes, while there is nothing in the wording of the ḥadīth which makes it objectionable.
You have likely heard that Shaykh al-Albānī has weakened the ḥadīth, as well as many other scholars.
There are a group of scholars that have authenticated it though, like al-Munthiree (Saahib at-Targheeb) and ad-Dimyaatee (Saahib al-Matjar), and the book you have quoted by Ibn al-Qayyim argues in favor of the meaning, while the author does not actually authenticate it.
I have a detailed gathering of the chains, but its part of my thesis, so I can't make it available right now. Especially since my work on this ḥadīth specifically is something that my supervisor has already disputed! Its quite an intricate case actually.
wa alaykumus-salāmu wa rahmatullaahi wa barakaatuh
The scholars have differed over the authenticity of the ḥadīth of prayer after using siwaak (miswaak) being better than prayer without it by 70 times.
There are many chains to the ḥadīth through a number of Companions, and in all of the chains there is weakness. There are some chains that need investigated from a lost book, "Kitaab as-Siwaak" of Abū Nu'aym. This book had dozens of chains for this ḥadīth and is thus extremely important for this discussion.
Anyway, the study of this ḥadīth is part of my thesis so I can't really go much further than this for now. In shaa' Allaah we'll start a new thread on it later.
The book you have attached has one of the longest discussions on the topic available. It has a beautiful defense of the meaning of the ḥadīth which refutes those who said the meaning is objectionable. While the author (Ibn al-Qayyim) does not actually authenticate the ḥadīth, he left it as a possibility to be investigated, showing that it would not be far-fetched to consider it acceptable. And Allaah knows best.