At very first note this is completely his opinion but if  he still love her then definitely he should give her a chance. Now, he should also put a condition before starting again the relationship that if she again disappoint him in any sought or she break the trust again he will not allow her to be his friend. Also, before starting the relation make her promise that every conflict should be sought and cleared before starting the next day. This will help both of them to work on the relation more and to maintain the trust. if the things are not soughed then this will again create mis-interpretations.