The phrase "hand of friendship" is a common expression that signifies a welcoming gesture or a sign of goodwill towards someone. However, if you're looking for alternative ways to convey the same message, there are plenty of synonyms to choose from. You could use phrases like "extend a helping hand," "offer an olive branch," "give a warm welcome," "show hospitality," "embrace with open arms," or "reach out with kindness." Each of these phrases communicates a similar sentiment of reaching out to someone with a friendly and welcoming gesture. So whether you're writing a heartfelt message to a friend or trying to connect with someone new, consider using one of these synonyms to convey your warm intentions.