In French, should we write «Je vous transmet» or « Je vous transmets » ?

When you write Je (te, lui, vous...) transmets, the verbe transmettre agrees with the subject je is spelled transmets: 

Je te transmets. <=> I pass on to you.

Je lui transmets. <=> I am passing on to him.

Je vous transmets. <=> I am passing on to you.

Je leur transmets. <=> I am passing on to them.

Je te le transmets. <=> I am passing it on to you.

Je le lui transmets. <=> I am passing it on to him.

Je vous le transmets. <=> I'm passing it on to you.

Je le leur transmets. <=> I am passing it on to them.

The fact that the complement is in the plural does not change the conjugation of the verb:

Je te les transmets. <=> I pass it on to you.

Je les lui transmets. <=> I pass it on to him.

Je vous les transmets. <=> I pass them on to you.

Je les leur transmets. <=> I pass them on to them.

Je te transmets les dossiers. <=> I'm passing the files on to you.

Je vous transmets quelques photos dans l'enveloppe. <=> I pass you some pictures in the envelope.

Je leur transmets les pièces complémentaires.<=> I pass them on to them.