Both is ok, but note two things:
- "Here is" is not »anbei«. "Here is" is »hier ist« (which sounds a little bit boring in German) and »anbei« is "enclosed".
- If you use für I also would add an article. (There already is an article contained in vom = von dem)
So this are versions you can use (in Germany and Switzerland:
Anbei die Rechnung vom Januar
Enclosed the invoice from January
Anbei die Rechnung für den Januar
Enclosed the invoice for January
If your customer lives in Austria, you have to know that the first month of the year has a different name in Austria. It is Jänner. So in Austria you better use this:
Anbei die Rechnung vom Jänner
Anbei die Rechnung für den Jänner
Januar will be understood in Austria too, but you can make your Austrian customers happy, if you use the name they use.
If you want to avoid complications with the month's name, write:
Anbei die Rechnung von 01/2017
Anbei die Rechnung für 01/2017
Note, that now you don't use an article, which turns vom (von dem) into von.
Difference between von and für
Die Rechnung für den Jänner/Januar
This means: The invoice contains items for the month January, i.e. it covers goods and services, that the customer consumed in this month. The date of the invoice's items is in January.
Die Rechnung vom Jänner/Januar
This means: The invoice was written in January. The date in the header of the invoice is a date in January.
(Thank you, user unknown for your comment)
You also can write:
Anbei die Jännerrechnung (A)
Anbei die Januarrechnung (D, CH)
Enclosed the January invoice
»Januarrechnung« and »Jännerrechnung« are compound nouns, built from the month's name and the word »Rechnung«. In German as well as in English here it is unclear, if it is the invoice from or for January.