How should the traveller pray?
If you have resolved to stay in the place to which you are travelling for more than four days, then you come under the same ruling as a resident from the moment you arrive there, so you have to do what the residents do, i.e., offer the prayers in full, and it is not permissible for you to shorten them.
You may shorten the prayers during the journey, but when you reach the place you should offer the prayers in full, because you come under the same ruling as a resident.
It says in Fataawa al-Lajnah al-Daa’imah (8/99): The kind of travel for which the concession of travel is prescribed is that which is regarded as travel according to custom, and the distance is approximately eighty kilometers. Whoever travels this distance or more may avail himself of the concessions for travellers, such as wiping over his socks for three days and two nights, joining and shortening prayers, and not fasting during Ramadaan. If this traveller intends to stay in a place for more than four days, then he should not avail himself of the concessions for travellers. If he intends to stay there for four days or less, then he may avail himself of the concessions for travellers. If a traveller stays in a place but does not know when he will finish his business and cannot state a certain length of time for his stay, then he may avail himself of the concessions for travelling even if he stays for a long time. It makes no difference whether he travels by land or by sea. End quote.
With regard to joining prayers, it is permissible for a traveller to join Zuhr and ‘Asr, and Maghrib and ‘Isha’, at the time of the earlier or later prayer, depending on what is easiest for him. But it is better for him not to do that unless it is difficult for him to offer every prayer on time.
Based on that, you can join two prayers together during the journey, but when you reach the place where you intend to stay for a month, then you should offer every prayer on time.
See also the answer to question no. 49885.
You should remember that prayer in congregation is obligatory for travellers as well as others. This has been explained in the answer to question no. 40299, so try to pray in congregation in the mosque.
And Allaah knows best.