Well, chico hasn't quite put it all together either!
Your statement "I had guessed memor as remember from mindful" is rather mystifying, Cathiron, but if you had guessed memor as 'mindful' it might have helped you see that amici is genitive singular, i.e. 'of a friend' not 'friends' or 'friendship', so: 'mindful of (your) friend'
And sis can mean 'please', but that is short for 'si vis', meaning 'if you will', which would mean there is no main verb here. So sis here must be the main verb - the subjunctive of 'es' 'you are', so: 'may you be'.
The whole thing "sis memor amici" would therefore be "May you be mindful of your friend". Or of course "Remember your friend".
So you guessed 'remember' all right, but 'friendship' or 'friends' are inappropriately free translations rather than 'very rough' approximations..